CaltechDATA: Book Chapter
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 11:00:44 -0700Stress-Strain Characteristics of Cohesionless Granular Materials Subjected to Statically Applied Homogeneous Loads in an Open System
https://resolver.caltech.edu/CaltechETD:etd-03242003-102726
Year: 1965
DOI: 10.7907/066B-HV20
A general stress-strain relationship in incremental and invariant form is derived for sand on the basis of experimental evidence. The resulting expression does not include the yield condition but makes allowance for the direction of loading and the state of stress. Two new modified and dimensionless invariant functions are introduced and a detailed description and classification of stress paths presented. A new first yield criterion for sand stressed to yield along one stress path is developed from experimental evidence. The friction angle in triaxial compression was minimum and 14[degrees] less than that in triaxial extension. The Mohr-Coulomb yield criterion extended to three dimensions is rejected.
Emphasis is placed on the importance of obtaining homogeneous stress in physical experiments. A new spherical compression apparatus was developed to study the behavior of sand under spherical compression. Disadvantages of former apparatuses were largely overcome by elimination of frictional loading, and a homogeneous state of stress was obtained. A new stress controlled three-dimensional compression apparatus capable of applying principal stresses to a rectangular, plate sample was developed to study the behavior of sand under a general stress state, particularly under deviatoric stress. This apparatus provided for the independent measurement of volumetric strain and allowed for the development of considerable deformation in obtaining yield.https://resolver.caltech.edu/CaltechETD:etd-03242003-102726Free and Forced Oscillations of a Class of Self-Excited Oscillators
https://resolver.caltech.edu/CaltechETD:etd-10012002-092546
Year: 1965
DOI: 10.7907/81MF-FT73
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Free and forced oscillations in oscillators governed by the equation [...] are studied with appropriate constraints on [...]. Theorems are proved on the existence and uniqueness of stable periodic solutions for free oscillations using the Poincare-Bendixson theory in the phase-plane. There follow several examples to illustrate the theorems and limit cycles are obtained for these examples by the Leinard construction. A result on the existence of periodic solutions in the forced case is obtained by use of Brouwer's fixed point theorem. The part on topological methods is concluded by applying Yoshizawa's results on ultimate boundedness of solutions to the forced case.
Approximate analytical solutions are obtained for specific examples for different regions of validity of the parameter [...]. For free oscillations, the perturbation solution is obtained for small [...]. A Fourier series approximation is given for other values of [...] and the limit cycle for the case [...] is obtained. Finally, the first order solution for forced oscillations is obtained by the method of slowly varying parameters and the stability of this solution is examined.https://resolver.caltech.edu/CaltechETD:etd-10012002-092546Theoretical Investigation of the Effect of Intramolecular Interactions on the Configuration of Polymeric Chains
https://resolver.caltech.edu/CaltechETD:etd-10072002-145049
Year: 1969
DOI: 10.7907/8KEP-R512
<p>A theoretical investigation of the effect of intramolecular interactions on the configurational statistics of a polymer molecule is presented. This problem has been studied by many authors and is known as the "excluded volume problem" in the literature. A statistical mechanical approach is used. Many of the similarities between the theory of "classical fluids" and the excluded volume problem are exploited.</p>
<p>The configurational statistics of 2 and 3 segment chains are computed exactly for the "hard sphere potential". The integrations were performed by introducing bipolar and tripolar coordinate systems. It was found that the mean square end-to-end distance for these cases was n<sup>1.33</sup> where n is the number of segments. These results are of no practical use in predicting the properties of real polymer chains which are much longer. It is instructive, however, to compare these exact results with approximate theories in the limit of short chain length.</p>
<p>A "cluster expansion" is written for the partition function of a polymer chain with the ends of the chain fixed. This is analogous to the cluster expansion for the partition function of an imperfect gas. The first-order term in this expansion is evaluated for the hard core potential. In the limit of small hard core diameters, the first-order term leads to the wellknown first-order perturbation theory for the mean square end-to-end distance. The exact results of this first-order correction term are used to construct higher-order terms of a specified "isolated topology". If only these terms are used in the cluster expansion, incorrect results are obtained for the mean square end-to-end distance. This indicates that higher-order terms of complicated topology are significant for longer chain length.</p>
<p>Various approximate integral equations for the restricted partition function of a polymer chain are presented. The most promising of these equations is the analog of the well-known Percus-Yevick equation in the theory of liquids. In deriving this equation two topologically distinct types of graphs are defined. These are the "nodal and elementary" graphs. An exact equation relating these types of graphs is presented. The analog of the Percus-Yevick approximation is made which leads to an integro-difference equation. This equation is solved exactly using the hard core potential for the special case of the hard core diameter equal to the polymer segment length. Results of numerical calculations are given for other intermediate values of this diameter ranging from zero to the segment length (the "pearl necklace" model). This leads to values of γ ranging correspondingly from 1.0 to 2.0 where <r<sup>2</sup><sub>1N</sub> ∝ M<sup>γ</sup>> with <r<sup>2</sup><sub>1N</sub> the mean square end-to-end distance and M the molecular weight. The numerical results for <r<sup>2</sup><sub>1N</sub> as a function of chain length are in good agreement with the second-order perturbation theory of Fixman for small hard core diameters.</p>https://resolver.caltech.edu/CaltechETD:etd-10072002-145049Minimum Energy Control of Electric Propulsion Vehicles
https://resolver.caltech.edu/CaltechETD:etd-10032002-120235
Year: 1969
DOI: 10.7907/24NJ-WQ58
Minimum-energy control problems for various electric propulsion vehicles are formulated and solved using modern control theory and systems engineering techniques. Analytical results are obtained by making several simplifications and approximations in the dynamical equations of each system whose performance index is related to the minimization of the system energy consumption for a required control action. An attempt is made to implement the resulting control laws using the current engineering practice.
https://resolver.caltech.edu/CaltechETD:etd-10032002-120235Self-similar elastodynamic solutions for the plane wedge
https://resolver.caltech.edu/CaltechETD:etd-11132006-080224
Year: 1977
DOI: 10.7907/E1D3-0T11
Wave propagation in a two-dimensional elastic wedge is fundamental to a large class of problems in elastodynamic theory, however until now analytical solutions to all but certain degenerate cases were unknown. In this thesis a general elastodynamic solution is derived for the wedge in a state of plane strain. Surface tractions are, restricted to uniform normal and shear loads spreading from the wedge vertex at constant velocity. The geometry and loading then allow self-similar solutions of the governing differential equations and boundary conditions in hyperbolic and elliptic domains. Hyperbolic solutions are found in terms of the elliptic solutions by the method of characteristics, while elliptic solutions are reduced using analytic function theory to two independent Fredholm integral equations of the second kind in one dimension. Although numerical solutions are beyond the scope of the investigation, the integral equations are solvable by standard techniques. Such solutions can be used to solve a number of plane elastodynamic problems involving an edge.https://resolver.caltech.edu/CaltechETD:etd-11132006-080224Discontinuous Deformation Gradients in Plane Finite Elastostatics of Incompressible Materials. (I) General Considerations. (II) An Example
https://resolver.caltech.edu/CaltechTHESIS:03012018-170438409
Year: 1979
DOI: 10.7907/seym-cd95
<p>This investigation is concerned with the possibility of the change of type of the differential equations governing finite plane elastostatics for <u>incompressible</u> elastic materials, and the related is sue of the existence of equilibrium fields with discontinuous deformation gradients. Explicit necessary and sufficient conditions on the deformation invariants and the material for the ellipticity of the plane displacement equations of equilibrium are established. The issue of the existence, locally, of "elastostatic shocks" -- elastostatic fields with continuous displacements and discontinuous deformation gradients -- is then investigated. It is shown that an elastostatic shock exists only if the governing field equations suffer a loss of ellipticity at some deformation. Conversely, if the governing field equations have lost ellipticity at a given deformation at some point, an elastostatic shock can exist, locally, at that point. The results obtained are valid for an arbitrary homogeneous, isotropic, incompressible, elastic material. In order to illustrate the occurrence of elastostatic shocks in a physical problem, a specific displacement boundary value problem is studied. Here, a particular class of isotropic, incompressible, elastic materials which allow for a loss of ellipticity is considered. It is shown that no solution which is smooth in the classical sense exists to this problem for certain ranges of the applied loading. Next, we admit solutions involving elastostatic shocks into the discussion and find that the problem may then be solved completely. When this is done, however, there results a lack of uniqueness of solutions to the boundary value problem. In order to resolve this non-uniqueness, dissipativity and stability are investigated.</p>https://resolver.caltech.edu/CaltechTHESIS:03012018-170438409Failure of Liquid Storage Tanks Due to Earthquake Excitation
https://resolver.caltech.edu/CaltechTHESIS:04132018-090928397
Year: 1981
DOI: 10.7907/m0v8-hs31
<p>Above ground liquid storage tanks have suffered serious damage during earthquakes. The damage of tanks can vary from local yielding or buckling of the tank wall, to loss of contents, or to collapse which leads to an unrepairable tank. Considerable work has been carried out on this problem with varying degree of success. However, the results are largely directed toward response rather than failure prediction. The information on failure mechanisms is very limited. The present work consists of scale model testing, correlation with existing analysis and failure prediction with laboratory verification. The scale model testing incorporates dynamic similarity of the fluid/structure interaction problem. The model study shows that small plastic models can be useful in studying the dynamics and buckling of liquid-filled tanks under ground excitation even though the model does not display complete similitude. The buckling criterion proposed in this study is based upon static considerations and the complex stress field in the shell wall is supplanted by a simple field for which analytical/experimental results are available. Harmonic buckling tests demonstrate that the static buckling criterion is satisfactory even though the prebuckling stress field is time dependent. The harmonic buckling tests, when correlated with the stresses from a response analysis, also indicate that the buckling is largely dependent upon the n = 1 response, Transient buckling tests are also carried out and the results show that the linear analysis together with the static buckling criterion gives a good prediction of the failure of a full fluid-filled tank. The test parameters in these buckling tests include water depth, title angle, thickness of tank wall, top end condition, ground excitation pattern, etc. In addition, buckling tests of unanchored tanks are conducted to study the influence of changing the anchorage of the tank base. An analytical model is suggested to predict the response of an unanchored tank due to overturning moment. The current design criterion of an unanchored tank is also assessed in this study. The results of this investigation, in addition to those carried out previously, provide a better understanding of the forced vibration problem, failure criterion and appropriate design procedure for a liquid storage tank.</p>
https://resolver.caltech.edu/CaltechTHESIS:04132018-090928397A Petrov-Galerkin Finite Element Formulation for Convection Dominated Flows
https://resolver.caltech.edu/CaltechETD:etd-02012005-161447
Year: 1981
DOI: 10.7907/Q164-VZ22
<p>In this thesis, a new finite element formulation for convection dominated flows is developed. The basis of the formulation is the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes. When implemented as a consistent Petrov-Galerkin weighted residual method, it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods.</p>
<p>The effectiveness of the streamline upwind/Petrov-Galerkin formulation for the linear advection diffusion equation is demonstrated with numerical examples. The formulation is extended to the treatment of the incompressible Navier-Stokes equations. An efficient implicit pressure/explicit velocity transient algorithm is developed which allows for several treatments of the incompressibility constraint and for multiple iterations within a time step. The algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a Reynolds number of 100.</p>https://resolver.caltech.edu/CaltechETD:etd-02012005-161447I. Propagating and Waiting Fronts in Nonlinear Diffusion. II. Sustained Reentry Roll Resonance
https://resolver.caltech.edu/CaltechETD:etd-09282006-094746
Year: 1981
DOI: 10.7907/bpk3-rt60
<p>Part I</p>
<p>We examine a nonlinear diffusion equation that arises in the study of a number of physical problems, where the equation is nonlinear because the diffusion coefficient is proportional to a power of the concentration. Previous authors have proven using similarity solutions, that this dependence produces fronts (interfaces between regions of zero and nonzero concentration) which propagate with finite speed, as well as waiting-time behavior, where the fronts remain stationary for a finite amount of time before beginning to move. These similarity solutions provide limited information about the solution for general initial conditions, however.</p>
<p>To alleviate this deficiency, we construct approximate solutions for the above nonlinear diffusion equation using singular perturbation theory. We do so by considering the equation in the limit of nearly linear diffusion, but the analysis reveals the basic qualitative behavior outside this limit as well.</p>
<p>The basic behavior follows from the leading-order approximation of a transformed equation, and propagating and waiting fronts are due to the formation (in this approximation) of what we call corner shocks. This enables us to determine for which initial conditions waiting time behavior will occur.</p>
<p>The transformed equation must be solved to first order to find the solution of the original equation to leading order, and when corner shocks occur at a point of nonzero concentration, this first order analysis shows that they become rounded (which we call a corner layer). When a corner shock occurs at a point of zero concentration, this rounding does not take place, and the corner shock remains sharp. This allows us to give a simple procedure for constructing approximate solutions of the nonlinear diffusion equation when corner shocks occur only at points of zero concentration.</p>
<p>Part II</p>
<p>We study a model of reentry roll resonance, a situation encountered when an almost axially symmetric vehicle reenters the earth's atmosphere, using the method of near identity transformations. This method allows us to extend previous results for the case of sustained resonance, when roll buildup occurs.</p>
<p>In particular, we give necessary conditions both for entrainmeat to sustained resonance and for sustained resonance to continue. These conditions imply that it is possible for sustained resonance to last for a finite time and then for unlocking of the resonance to occur. In addition, from the analysis we make a conjecture concerning sufficient conditions for sustained resonance.</p>https://resolver.caltech.edu/CaltechETD:etd-09282006-094746Dynamic Centrifuge Testing of Cantilever Retaining Walls
https://resolver.caltech.edu/CaltechETD:etd-12132006-104119
Year: 1982
DOI: 10.7907/vep9-1127
<p>An investigation was made into the behavior of flexible cantilever walls retaining a cohesionless soil backfill and subjected to earthquake-type dynamic excitations using the centrifuge modelling technique. The study was motivated by the abundant observations of earth retaining structure damage and failures documented in earthquake damage reports.</p>
<p>The "prototype" typical walls were designed using the traditional Mononobe-Okabe dynamic lateral earth pressure theory, were properly scaled for use in the centrifuge at 50 g's and were subjected to lateral earthquake-like motions which were considered to be of realistic levels. The walls were amply instrumented with pressure and displacement transducers, accelerometers, and strain gages. Moment, pressure, shear, and displacement distributions (static, dynamic, and residual) were obtained.</p>
<p>From the test data, some empirical curves for relating the upper bound responses of the retaining walls to the strong motion characteristics of the applied earthquakes were obtained.</p>https://resolver.caltech.edu/CaltechETD:etd-12132006-104119An Experimental Investigation into the Mechanics of Dynamic Fracture
https://resolver.caltech.edu/CaltechETD:etd-10302003-104624
Year: 1982
DOI: 10.7907/ZSX5-Q128
<p>Current theories of dynamic fracture are based on elastodynamic analyses of mathematically sharp plane cracks and as such do not explain the observed terminal velocities or the phenomenon of crack branching satisfactorily. The present investigation addresses the above problems by using both microscopic and macroscopic interpretations. The experimental scheme that is used in this investigation is the configuration of a pressure loaded semi-infinite crack in an infinite medium. The loading is achieved through an electromagnetic device which provides highly repeatable loading. The method of caustics is used in conjunction with a high speed camera to obtain the time histories of the crack tip stress intensity factor and the crack position.</p>
<p>The problems of crack initiation and crack arrest are explored. The stress intensity factor at initiation is found to be independent of the rate of applied loading when the latter is below about 10<sup>4</sup>MPA/sec, but the initiation stress intensity factor increases considerably when the loading rate is increased further. Crack arrest is obtained in large specimen by using very low energy loading pulses. It was found that the stress intensity factor at crack arrest was constant and also that, within the time resolution of the high speed camera (5 μsec), the crack comes to a stop abruptly.</p>
<p>The crack propagation and branching aspects were investigated first using post-mortem analysis of the fracture surfaces and high speed photomicrography to get an idea of the microscopic processes that occur in the fracure process. From this investigation, it was found that crack propagation involving high stress intensity factor and high velocity situations takes place by the growth and interaction of microcracks, due to the voids present in the material. A surprising result of this investigation was that cracks propagated at a constant velocity, although the stress intensity factor varied. Current theories of dynamic fracture cannot explain such behaviour. The crack branching process was found to be a continuous process arising out of propagation along a straight line. High speed photomicrographs of the branching process indicated the presence of a number of part-through attempted branches that interact with one another and finally the successful emergence of a few full fledged branches.</p>
<p>The microscopic observations on the crack propagation and branching process leads to a new interpretation of dynamic fracture that attempts to qualitatively explain the constancy of the velocity of propagation, the terminal velocity and crack branching. The crack branching mechanism is a logical continuation of the mechanism for crack propagation.</p>
https://resolver.caltech.edu/CaltechETD:etd-10302003-104624Direct Output Feedback Control of Large Flexible Spacecraft
https://resolver.caltech.edu/CaltechETD:etd-12082005-143337
Year: 1982
DOI: 10.7907/vx2f-yh14
<p>This report addresses the problem of active control of large flexible space structures. The current activities and control schemes in this field are briefly reviewed. A direct output feedback control (DOFC) technique is proposed to control the large flexible space structures. Assuming an N-degree-of-freedom system with n collocated sensor and actuator (S/A) pairs, where N is typically much larger than n, the analysis shows that at least the first n lowest critical vibration modes can be controlled with the system remaining stable. A formula for the selection of the feedback control gain matrix is provided. The DOFC approach is also applicable to the systems with certain types of nonlinearities, as well as systems including sensor/actuator dynamics. A simple criterion for selecting the "optimal" location of collocated sensor and actuator pairs is proposed. Numerical examples are given to illustrate the proposed DOFC technique and the "optimal" location criterion.</p>https://resolver.caltech.edu/CaltechETD:etd-12082005-143337A New Model for Three-Dimensional Nonlinear Dispersive Long Waves
https://resolver.caltech.edu/CaltechETD:etd-09232005-153011
Year: 1982
DOI: 10.7907/05SA-9135
<p>A new formulation of the pair of Boussinesq-class equations for modelling the propagation of three-dimensional nonlinear dispersive long water waves is presented. This set of model equations permits spatial and temporal variations of the bottom topography. Further, the two resultant equations may be combined into a single equation through the introduction of an irrotational layer-mean velocity. An exact permanent-form solution is derived for the combined equation, which is still of the Boussinesq-class and includes reflection. This solution for the surface height is found to describe a slightly wider wave than the permanent form solution to the uni-directional Korteweg-deVries Equation.</p>
<p>A numerical scheme using an implicit finite-difference method is developed to solve the combined equation for propagation over fixed sloping bottom topography. The scheme is tested for various grid sizes using the permanent-form solution, and an oscillatory tail is seen to develop as a result of insufficient mesh refinement.</p>
<p>Several cases of wave propagation over a straight sloping ramp onto a shelf are solved using the permanent-form solution as initial conditions and the results are found to be in good agreement with previous results obtained by using either the Boussinesq dual-equation set or the single Korteweg-deVries equation. The combined equation is used to solve the related problem in two horizontal dimensions of a wave propagating in a channel having a curved-ramp bottom topography. Depending on the specific topography, focussing or defocussing occurs and the crest is selectively amplified. Indications of cross-channel oscillation are presented. Linear, nondispersive theory is used to solve a case with identical topographical features and initial condition. The solutions using the simplified theory are found to be considerably different from the results for nonlinear, dispersive theory with respect to the overall three-dimensional wave shape as well as in the areas of crest amplification, soliton formation and cross-channel effects.</p>https://resolver.caltech.edu/CaltechETD:etd-09232005-153011The Analysis of a Nonlinear Difference Equation Occurring in Dynamical Systems
https://resolver.caltech.edu/CaltechETD:etd-07082005-102658
Year: 1982
DOI: 10.7907/X17F-E253
<p>A difference equation with a cubic nonlinearity is examined. Using a phase plane analysis, both quasi-periodic and chaotically behaving solutions are found. The chaotic behavior is investigated in relation to heteroclinic and homoclinic oscillations of stable and unstable solution manifolds emanating from unstable periodic points. Certain criteria are developed which govern the existence of the stochastic behavior. An approximate solution technique is developed giving expressions for the quasi-periodic solutions close to a stable periodic point and the accuracy of these expressions are investigated. The stability of the solutions is examined and approximate local stability criteria are obtained. Stochastic excitation of a nonlinear difference equation is also considered and an approximate value of the second moment of the solution is obtained.</p>https://resolver.caltech.edu/CaltechETD:etd-07082005-102658Dynamic Behavior of Rocking Structures Allowed to Uplift
https://resolver.caltech.edu/CaltechTHESIS:05162018-151856693
Year: 1982
DOI: 10.7907/jexq-jr68
<p>Strong shaking of structures during large earthquakes may result in some cases in partial separation of the base of the structure from the soil. This phenomenon of uplifting, which can affect the dynamic behavior of the structure significantly, even if the amount of uplift is small, is examined in this thesis. First the case of a rocking rigid block is investigated and then more complicated, flexible superstructures are introduced. Two foundation models which permit uplift are considered: the Winkler foundation and the much simpler "two-spring" foundation. Several energy dissipating mechanisms are also introduced into these models. It is shown that an equivalence between these two models for the foundation can be established, so that one can always work with the much simpler two-spring foundation. In this way complete analytical solutions can be derived in most cases. Moreover, simple approximate methods for the calculation of the apparent fundamental period of the rocking system are developed and simplified methods of analysis are proposed.</p>
<p>In general, uplift leads to a softer vibrating system which behaves nonlinearly, although the response is composed of a sequence of linear responses. As a result, the apparent fundamental resonant frequency of the uplifting system is always less than the fundamental resonant frequency of both the soil-structure interacting system, in which lift-off is not allowed, and the superstructure itself. The second and higher resonant frequencies of the superstructure, however, are not affected significantly by lift-off. For damped foundations, the ratio of critical damping associated with the apparent fundamental mode decreases, in general, with the amount of lift-off. These effects of uplift on the dynamic properties of the rocking system can alter the response of the structure significantly during an earthquake. Nevertheless, it cannot be said a priori whether they are favorable to the behavior or not; this depends on the parameters of the system and the time history of the excitation.</p>https://resolver.caltech.edu/CaltechTHESIS:05162018-151856693Passive and Active Control of Boundary Layer Transition
https://resolver.caltech.edu/CaltechETD:etd-09182006-135720
Year: 1982
DOI: 10.7907/CKFA-E875
<p>It is well known that laminar-turbulent boundary layer transition is initiated by the formation of Tollmien-Schlichting laminar instability waves. The amplification rates of these waves are strongly dependent on the shape of the boundary layer velocity profile. Consequently, the transition process can be controlled by modifying the velocity profile. This can be accomplished by controlling the pressure gradient (dp/dx), using boundary layer suction, installing surface roughness elements, or by surface heating or cooling. Methods used to modify the transition process through changes in the mean velocity profile are called "passive" in this paper. There exists a large set of experiments and theory on the application of passive methods for boundary layer control. In the present work only surface heating will be addressed.</p>
<p>Transition measurements were made on a heated flat plate in water. Results are presented for several plate wall temperature distributions. An increase by a factor of 2.5 in transition Reynolds number was observed for a 5°C isothermal wall overheat. Buoyancy effects on transition were minimal due to the small Richardson and Grashof numbers encountered in the experiments.</p>
<p>The amplification of laminar instability waves is comparatively to process, taking place over many boundary layer thicknesses. After the slow amplification of the laminar instability waves, transition occurs by a strong three dimensional dynamic instability. It appears possible to attenuate (or reinforce) the instability waves by introducing amplitude-and phase-controlled perturbations into the laminar boundary layer using feedback control system. This method is called "active" control and forms the larger part of the research reported in this thesis.</p>
<p>A combination of sensors, activators and feedback control electronics is required for active control. The sensors used in the experiments are flush-mounted hot film wall shear robes. A new type of activator was developed using thin, flush-mounted surface heating elements to excite instability waves in the laminar boundary layer by periodic (active) heating.</p>
<p>Experimental evidence is presented illustrating the effects of periodically heated flush mounted strips in perturbing a flat plate boundary layer in water. The results of superposition of forced laminar instability waves are also given. Finally, an active feedback-control system using a single hot film probe and strip heater was developed to control natural laminar instability waves in real time. It is shown that when the natural waves were attenuated, the transition length was increased by 25%, requiring only 10 watts of strip heater power. To accomplish the same transition delay using passive heating, the internal heating pads had to supply 1900 watts of power.</p>https://resolver.caltech.edu/CaltechETD:etd-09182006-135720Finite Plane and Anti-Plane Elastostatic Fields with Discontinuous Deformation Gradients Near the Tip of a Crack
https://resolver.caltech.edu/CaltechETD:etd-09122006-153033
Year: 1982
DOI: 10.7907/td0f-kr59
<p>In this paper the fully nonlinear theory of finite deformations of an elastic solid is used to study the elastostatic field near the tip of a crack. The special elastic materials considered are such that the differential equations governing the equilibrium fields may lose ellipticity in the presence of sufficiently severe strains.</p>
<p>The first problem considered involves finite anti-plane shear (Mode III) deformations of a cracked incompressible solid. The analysis is based on a direct asymptotic method, in contrast to earlier approaches which have depended on hodograph procedures.</p>
<p>The second problem treated is that of plane strain of a compressible solid containing a crack under tensile (Mode I) loading conditions. The material is characterized by the so-called Blatz-Ko elastic potential. Again, the analysis involves only direct local considerations.</p>
<p>For both the Mode III and Mode I problems, the loss of equilibrium ellipticity results in the appearance of curves ("elastostatic shocks") issuing from the crack-tip across which displacement gradients and stresses are discontinuous.</p>
https://resolver.caltech.edu/CaltechETD:etd-09122006-153033Ordinary and Strong Ellipticity in the Equilibrium Theory of Incompressible Hyperelastic Solids
https://resolver.caltech.edu/CaltechETD:etd-11012005-130640
Year: 1983
DOI: 10.7907/jzka-ce91
<p>In this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three-dimensional field equations in the nonlinear equilibrium theory of incompressible, homogeneous and isotropic, hyperelastic solids. The resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain-energy density with respect to the deformation invariants or the principal stretches. The conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the Baker-Ericksen inequalities and possess a positive shear modulus at infinitesimal deformations. Various implications of these ellipticity conditions for special classes of materials and deformations are explored.</p>https://resolver.caltech.edu/CaltechETD:etd-11012005-130640An Engineering Analysis of Polymer Film Adhesion to Rigid Substrates
https://resolver.caltech.edu/CaltechETD:etd-05152007-111322
Year: 1983
DOI: 10.7907/3GQW-YP87
<p>An important source of interface fracture contributing to adhesive failure in a bimaterial sandwich, consisting of a rigid substrate and a viscoelastic encapsulant material, arises from residual stresses. The encapsulant is often deposited on the substrate above its glass transition temperature region but used below this temperature range. In order to determine the magnitude of the residual stresses a viscoelastic stress analysis of a bimaterial sandwich is carried out, taking into account the time-dependent material properties of the polymeric layer and the environmental "loading" conditions. The theoretical analysis is paralleled by an experimental examination of the time-dependent out-of-plane deformation of thin, circular sandwiches.</p>
<p>Polyvinyl acetate was chosen as a model material exhibiting significant viscoelastic effects under room test conditions. Therefore the pertinent physical and mechanical properties of PYA<sub>c</sub> are determined; these include the thermal coefficient of expansion, the shear creep compliance and the relaxation modulus. In the experimental work BK-7 glass is taken as the "rigid" substrate. The measurements connected to the stress analysis are monitored with laser interferometry (Newton's rings). A comparison between theory and experiment completes the viscoelastic stress analysis.</p>
<p>In the second part of this study time dependent adhesive failure of rubbery materials is investigated. Polymeric materials are being used increasingly for a wide variety of applications. Some of these materials are applied as protective layers to isolate their substrates from a hostile environment. Others achieve remarkable structural bond strengths thereby displacing the traditional mechanical fasteners like bolts and rivets. If one wants to investigate the long time integrity of a layer assembly the time dependence of the material properties of the adhesives needs to be carefully analyzed. This time dependence is also reflected in the energy required to create new surfaces as interfacial debonding proceeds the adhesive fracture energy is one of the dominant parameters in time dependent adhesive failure. In our investigation it is characterized through peel testing.</p>
<p>With the knowledge of the pertinent material properties as well as of the adhesive fracture energy, we then proceed to formulate a criterion for continuing interfacial crack propagation. The analysis is carried out for elastic solids, with the effect of viscoelastic behavior incorporated later on. Debond tests provide a way to check how well the theoretical predictions correspond to experimental debond results.</p>https://resolver.caltech.edu/CaltechETD:etd-05152007-111322Optimal Low Thrust, Three Burn Orbit Transfers with Large Plane Changes
https://resolver.caltech.edu/CaltechETD:etd-08152005-091409
Year: 1983
DOI: 10.7907/NXPK-GE17
<p>During the last twenty-five years, much attention has been devoted to the problem of optimal orbit transfer. The problem has been conveniently divided into two categories - unlimited thrust (or acceleration) orbit transfers and limited thrust (or acceleration) orbit transfers. The unlimited thrust orbit transfers use infinite thrust, zero burn time burns and hence have also come to be known as impulsive burn orbit transfers. In general it has been found that optimal (i.e., minimum fuel, time-free) solutions to these types of transfers require two or possibly three burns. The limited thrust transfers, in contrast, do not use impulsive burns but use burns which have a finite thrust level and a nonzero burn time and, hence, are also known as finite burn orbit transfers.</p>
<p>If our attention is restricted to finite multi-burn transfers which have burn times less than an orbital period, two classes of transfers emerge. These classes of transfers are either Geometrically Similar to the 2-Burn Impulsive (GS2BI) transfers or Geometrically Similar to the 3-Burn Impulsive (GS3BI) transfers. For example, if a 2-burn impulsive solution has a perigee burn followed by an apogee burn, the GS2BI finite burn transfer would use one or more perigee burns followed by one or more apogee burns.</p>
<p>Recent-studies have presented optimal solutions to GS2BI finite burn orbit transfers for various thrust to weight ratios. The current study presents the optimal solutions to GS3BI finite burn orbit transfers between a 28.5° inclined low-earth orbit and a series of 63.4° inclined circular orbits and a series of 63.4° inclined elliptical orbits with twelve hour periods. Also presented are optimal solutions to GS3BI finite burn orbit transfers between 97° inclined high-earth orbits and a 57° inclined low-earth orbit. Optimal solutions are found to be bounded by a lower limit on the initial thrust to weight ratio. It is shown that as the final perigee altitude is increased, the GS3BI finite burn transfer degenerates to a GS2BI finite burn transfer much as it would for the impulsive case.</p>
<p>Analysis of the optimal steering during various burns reveals a natural division of the steering strategies into two categories based on whether a burn results in a predominant change in the orbit size-or-the orbit plane. The similarity of these optimal steering strategies to previously obtained simple "near-optimal" steering strategies is discussed.</p>https://resolver.caltech.edu/CaltechETD:etd-08152005-091409An Empirical Model for Vortex-Induced Vibrations
https://resolver.caltech.edu/CaltechTHESIS:09272018-115401142
Year: 1983
DOI: 10.7907/T3ZS-SH29
<p>Through an analytical-empirical approach, the vortex-excited transverse oscillations of flexibly-mounted circular cylinders in a uniform flow is studied.</p>
<p>A new model is derived, assuming spanwise constant flow velocity within the sub-critical range of Reynolds numbers and using only experimental data obtained from forced cylinders in water.</p>
<p>The steady-state response of flexibly-mounted cylinders is obtained as a function of the structural system and flow parameters and its stability is analyzed. Several characteristics observed experimentally and also present in the model response are discussed.</p>
<p>The resultant model's capability for predicting structural response for a wide range of fluid mediums is illustrated through comparisons between model predictions and results obtained experimentally from flexibly-mounted cylinders in air and in water.</p>
<p>This model developed is expected to yield better results for structures in water, by virtue of being based only on experimental results obtained in water.</p>https://resolver.caltech.edu/CaltechTHESIS:09272018-115401142Analysis and Control of Quasi Distributed Parameter Systems
https://resolver.caltech.edu/CaltechETD:etd-08092005-091223
Year: 1983
DOI: 10.7907/96PH-6521
<p>As engineering systems become larger and more flexible, serious consideration must be given to the very high order, and consequently very high bandwidth, of these so called quasi-distributed parameter systems. In particular, as practical active control devices such as sensors and actuators have finite bandwidth, great care must be exercised so that control of low frequency modes does not cause instability of intermediate and high frequency modes. In this report, the nature of these stability problems is investigated in the context of direct velocity feedback control, and approximate bounds on the diagonal elements of the modal gain matrix are derived. Two velocity feedback techniques are proposed to alleviate potential instability, but these are dependent on the natural damping of the system, which remains uncertain in practice. Another technique using position feedback is considered. Despite certain additional complications, position feedback control proves to be more advantageous in many ways than velocity feedback. Some preliminary analyses on a quasi-linear vibration suppression technique via damping matrix modification are also presented. The feasibility of these theoretical techniques are confirmed by means of a numerical simulation on a simply supported discrete shear beam.</p>
https://resolver.caltech.edu/CaltechETD:etd-08092005-091223Two Problems in Plane Finite Elastostatics
https://resolver.caltech.edu/CaltechETD:etd-09182006-085128
Year: 1983
DOI: 10.7907/yhjy-mb48
<p>In this paper the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids is used to study the elastostatic fields in plane strain near the point of application of a concentrated force on a deformed half plane and near the vertex of a circular sector whose plane deformed faces are subjected to prescribed tractions.</p>
<p>In the concentrated force problem, restricting only the form of the elastic potential at large extensional deformations, it is shown that, for materials which "harden" in simple shear, the displacement is bounded at the point of application of the load. This is not the case for materials which "soften" in shear. Estimates of the true stress tensor near the singular point are given.</p>
<p>In the sector problem, for a class of the materials mentioned, the deformation and stress field near the vertex of the deformed cross-section are derived and discussed.</p>
https://resolver.caltech.edu/CaltechETD:etd-09182006-085128The Emergence and Propagation of a Phase Boundary in an Elastic Bar
https://resolver.caltech.edu/CaltechETD:etd-09052006-154543
Year: 1983
DOI: 10.7907/85D8-5A19
<p>This dissertation is concerned with the dynamical analysis of an elastic bar whose stress-strain relation is not monotonic. Sufficiently large applied loads then require the strain to jump from one ascending branch of the stress-strain curve to another such branch. For a special class of these materials, a nonlinear initial-boundary value problem in one-dimensional elasticity is considered for a semi-infinite bar whose end is subjected to either a monotonically increasing prescribed traction or a monotonically increasing prescribed displacement. If the stress at the end of the bar exceeds the value of the stress at any local maximum of the stress-strain curve a strain discontinuity or "phase boundary" emerges at the end of the bar and subsequently propagates into the interior. For classically smooth solutions away from the phase boundary, the problem is reducible to a pair of differential-delay equations for two unknown functions of a single variable. The first of these two functions gives the location of the phase boundary, while the second characterizes the dynamical fields in the high-strain phase of the material. In these equations the former function occurs in the argument of the latter, so that the delays in the functional equations are unknown. A short-time analysis of this system provides an asymptotic description of the emergence and initial propagation of the phase boundary. For large-times, a different analysis indicates that the phase boundary velocity approaches a constant which depends on material properties and on the ultimate level reached by the applied load as well. Higher order corrections depend on the detailed way in which the load is applied. Estimates for the various dynamical field quantities are given and a priori conditions are deduced which determine whether the phase boundary eventually becomes the leading disturbance.</p>https://resolver.caltech.edu/CaltechETD:etd-09052006-154543A General Solution Strategy for Large Scale Static and Dynamic Nonlinear Finite Element Problems Employing the Element-by-Element Factorization Concept
https://resolver.caltech.edu/CaltechETD:etd-09012006-080048
Year: 1983
DOI: 10.7907/jqbq-rc43
<p>It is proposed to solve large-scale finite-element equation systems arising in structural and solid mechanics by way of an element-by-element approximate factorization technique which obviates the need for a global coefficient matrix. The procedure has considerable operation count and I/O advantages over direct elimination schemes and it is easily implemented. Numerical results demonstrate the effectiveness of the method and suggest its potential for the analysis of large-scale systems.</p>https://resolver.caltech.edu/CaltechETD:etd-09012006-080048The Propagation and Arrest of an Edge Crack in an Elastic Half-Space Under Conditions of Anti-Plane Shear: Analytical and Numerical Results
https://resolver.caltech.edu/CaltechETD:etd-09052006-082841
Year: 1983
DOI: 10.7907/jb3j-5460
<p>The motion of an edge crack extending non-uniformly in an elastic half-space under conditions of anti-plane shear is analyzed. An expression for the stress intensity factor at the crack tip is obtained, and an energy balance crack propagation criterion is used to find the equation of motion of the tip. On solving this equation numerically, it is found that crack arrest occurs before the second reflected wave from the boundary reaches the tip.</p>
<p>In the second half of this investigation, a numerical procedure for studying anti-plane shear crack propagation problems using finite differences is developed. To approximate the elastodynamic field as accurately as possible near the moving crack tip, where singular stresses occur, the local asymptotic displacement field near the tip is incorporated into the finite difference scheme. The numerical procedure is applied to the edge crack problem analyzed in the first part of this study, and the numerical and exact results are compared.</p>https://resolver.caltech.edu/CaltechETD:etd-09052006-082841Element-by-Element Solution Procedures for Nonlinear Transient Heat Conduction Analysis
https://resolver.caltech.edu/CaltechETD:etd-01252007-132425
Year: 1984
DOI: 10.7907/G7VB-EV65
<p>Despite continuing advancements in computer technology, there are many problems of engineering interest that exceed the combined capabilities of today's numerical algorithms and computational hardware. The resources required by traditional finite element algorithms tend to grow geometrically as the "problem size" is increased. Thus, for the forseeable future, there will be problems of interest which cannot be adequately modeled using currently available algorithms. For this reason, we have undertaken the development of algorithms whose resource needs grow only linearly with problem size. In addition, these new algorithms will fully exploit the "parallel-processing" capability available in the new generation of multi-processor computers.</p>
<p>The approach taken in the element-by-element solution procedures is to approximate the global implicit operator by a product of lower order operators. This type of "product" approximation originated with ADI techniques and was further refined into the "method of fractional steps." The current effort involves the use of a more natural operator split for finite element analysis based on "element operators." This choice of operator splitting based on element operators has several advantages. First, it fits easily within the architecture of current FE programs. Second, it allows the development of "parallel" algorithms. Finally, the computational expense varies only linearly with the number of elements.</p>
<p>The particular problems considered arise from nonlinear transient heat conduction. The nonlinearity enters through both material temperature dependence and radiation boundary conditions. The latter condition typically introduces a "stiff" component in the resultant matrix ODE's which precludes the use of explicit solution techniques. Implicit solution techniques can be prohibitively expensive. Instead, the matrix equations are solved by combining a modified Newton-Raphson iteration scheme with an element-by-element preconditioned conjugate gradient subiteration procedure. The resultant procedure has proven to be both accurate and reliable in the solution of medium-size problems in this class.</p>
https://resolver.caltech.edu/CaltechETD:etd-01252007-132425Investigation of Local Geology Effects on Strong Earthquake Ground Motions
https://resolver.caltech.edu/CaltechTHESIS:12122018-092221333
Year: 1984
DOI: 10.7907/pm3k-w086
<p>Accelerograms recorded at four stations in the Pasadena area during the 1971 San Fernando, the 1970 Lytle Creek, the 1968 Borrego Mountain and the 1952 Kern County earthquakes are analyzed to investigate local geology effects on strong earthquake ground motions. Spatial variations of the ground motions at two nearby stations are also investigated. It is found that the ground motions in this area caused by the local geology effects depend on the 3- dimensional configuration of the local geology and the direction of arriving seismic waves. Local geology effects are less evident on the leading portions of the accelerograms than the trailing portions, indicating the effects of local geology on surface wave propagations. Comparison of the Fourier amplitudes of the motions recorded at the same station during different earthquakes shows that there are no significant spectral peaks can be identified as site periods. Hence, it is not appropriate to characterize such local sites by a site period.</p>
<p>A two-dimensional model considering inclined propagating P and S waves in a horizontal-layered structure, which is more realistic and closer to the actual seismic environment within a local geology than the one-dimensional model of vertically propagating waves, is studied. The transfer functions between the free surface and the half-space outcrop for a single incident P, SV or SH wave from the half-space at an incident angle are defined and derived by a matrix method. Two numerical examples are given to demonstrate the effects of incident angle and material damping on the transfer function. It is found that the transfer function between the free surf ace motions and the bedrock outcrop motions to multiple incident waves having different amplitudes, angles and arrival times is quite different from that for a single incident wave. Completely satisfactory results cannot be expected when using the analytical model for evaluating the local geology effects on the motions during a nearby shallow-focus earthquake for which seismic waves emitted from different parts of the fault will approach the bedrock from different directions and at different angles.</p>
<p>The analytical model for assessing local geology effects is evaluated in the light of the data recorded at stations in the Pasadena area during the 1971 San Fernando earthquake. The observed site transfer functions between the alluvial and the rock sites are obtained and compared with the computed results from a two-dimensional model with 7-layers overlying a half-space. Values of model parameters are optimally adjusted to give a best least-squares fit between computed and observed amplitude ratios. It is concluded that the analytical model oversimplifies the local geological structure in the Pasadena area and the actual seismic environment in the area during the 1971 San Fernando earthquake.</p>
<p>It is concluded from these studies that the effects of the source mechanism and the seismic wave travel paths upon the site ground motion can be comparable to the effect of the local geology. The characteristics of the source mechanism, such as type of faulting, direction of fault-slip propagation, nature of stress drop across the fault surface, orientation of fault, depth beneath ground surface, etc., can appreciably influence the ground motion at the site. Also, the travel path can have a significant effect through influencing the types of waves that reach the site, and the directions of approach of the waves. The results of this study indicate that a better understanding of the spatial variation of ground motions, of the role played by different types of waves and their contributions to an accelerogram, and of the propagation directions of the waves is needed for assessing local geology effects on earthquake ground motions. A local array is desirable to provide data for giving a reasonably complete picture of the nature of ground motions in a local area.</p>https://resolver.caltech.edu/CaltechTHESIS:12122018-092221333Evaluation of the Unsteady Effects for a Class of Wind Turbines
https://resolver.caltech.edu/CaltechETD:etd-11082005-093825
Year: 1984
DOI: 10.7907/JVZE-1485
<p>An investigation of a class of vertical axis wind turbines is carried out with the unsteady effects due to the rotating blade motion fully taken into account. The work is composed of two parts.</p>
<p>In part one, a hydromechanical theory is developed which proceeds from the point of view of unsteady airfoil theory. A rotor comprised of a single blade is used and a two-dimensional analysis is applied to a cross section of the rotor in the limiting mode of operation wherein U « ΩR. Use of linearized theory and of the acceleration potential allows the problem to be expressed in terms of a Riemann-Hilbert boundary value problem. The method of characteristics is used to solve for the remaining unknown function. A uniformly valid first order solution is obtained in closed form after some approximation based on neglecting the variations in the curvature of the path. Explicit expressions of the instantaneous forces and moments acting on the blade are given and the total energy lost by the fluid and the total power input to the turbine are determined.</p>
<p>In part two, the lift acting on a wing crossing a vortex sheet is evaluated by application of a reciprocity theorem in reverse flow. This theorem follows from Green's integral theorem and relates the circulation around a blade having impulsively crossed a vortex wake to the lift acting on a blade continuously crossing a vortex wake. A solution is obtained which indicates that the lift is composed of two parts having different rates of growth, each depending on the apparent flow velocity before and after the crossing.</p>https://resolver.caltech.edu/CaltechETD:etd-11082005-093825Application of Plasticity Theory to Soil Behavior: A New Sand Model
https://resolver.caltech.edu/CaltechETD:etd-12212005-143343
Year: 1984
DOI: 10.7907/Z23J-9E80
<p>The representation of rheological soil behavior by constitutive equations is a new branch of soil mechanics which has been expanding for 30 years. Based on continuum mechanics, numerical methods (finite elements) and experimental techniques, this new discipline allows practicing engineers to solve complex geotechnical problems. Although all soils are constituted of discrete mineral particles, forces and displacements within them are represented by continuous stresses and strains. Most stress-strain relationships, which describe the soil behavior, are derived from plasticity theory. Originated for metals, the conventional plasticity is presented and illustrated simultaneously with a metal and a soil model. Each plasticity concept may be criticized when applied to soil. A recent theory, called "bounding surface plasticity," generalizes the conventional plasticity and describes more accurately the cyclic responses of metals and clays. This new theory is first presented and linked with the conventional plasticity, then applied to a new material, sand. Step by step a new sand model is constructed, mainly from data analysis with an interactive computer code. In its present development, only monotonic loadings are investigated. In order to verify the model ability to describe sand responses, isotropic, drained and undrained tests on the dense Sacramento River sand are simulated numerically and compared with real test results and predictions with another model. Finally the new constitutive equation, which was formulated in the p-q space for axisymmetric loadings, is generalized in the six-dimensional stress state with the assumption of isotropy and a particular Lode's angle contribution. This new model is ready to be used in finite element codes to represent a sand behavior.</p>https://resolver.caltech.edu/CaltechETD:etd-12212005-143343An Experimental Study of Convective Heat Transfer, Friction, and Rheology for Non-Newtonian Fluids: Polymer Solutions, Suspensions of Fibers, and Suspensions of Particulates
https://resolver.caltech.edu/CaltechETD:etd-03272007-105407
Year: 1985
DOI: 10.7907/pr91-d523
<p>An experimental investigation was conducted on the convective heat transfer, friction, and rheological properties of various types of non-newtonian fluids in circular tube flows.</p>
<p>If an apparent Reynolds number is used and if the temperature and degradation effects are properly taken into account, the reduced turbulent friction and heat transfer results, respectively, are then shown to be well correlated by the same expressions for different fluids, regardless of the nature of the fluids and whether they are shear-thinning or shear-thickening. This representation can also separate the reductions in turbulent heat transfer and friction that are induced by viscoelasticity from those induced by pseudoplasticity.</p>
<p>Polyacrylamide solutions inducing asymptotic and intermediate drag reduction regimes were investigated over a broad range of Reynolds numbers. The minimum heat transfer asymptote was determined for fully-developed conditions and for the very long (up to x/D = 600) entrance region observed. Solutions subjected to various degrees of intentional pre-degradation were studied to separate this effect from that of the degradation induced in the test tube itself.</p>
<p>A kerosene-based antimisting polymer solution was also studied. It was found to exhibit a complex viscous behavior involving time-dependency, shear-thickening beyond a critical shear rate, high susceptibility to degradation, and large sensitivity to temperature variations. The unusual friction and heat transfer results obtained with this fluid were, however, reduced to simple correlations for asymptotic drag reduction if an appropriate computational model is used.</p>
<p>Suspensions of bentonite of various concentrations were investigated in laminar and turbulent regimes, and the results for fully-developed and entrance flows were well correlated by newtonian relationships when an adequate wall viscosity concept was used. A combination of bentonite and polymer was found to be unusually susceptible to mechanical degradation, which affected significantly the viscosity and the level of drag and heat transfer reductions obtained.</p>
<p>A suspension of organic pulp based on tomato puree was shown to exhibit up to 40% of viscoelastic-type reduction in heat transfer and friction coefficients with respect to newtonian fluids in the turbulent regime. For laminar flow, however, these coefficients were larger than expected. Combinations of pulp and polymer were investigated as well.</p>
<p>A method was developed to predict the "diameter effect" for viscoelastic fluids.</p>https://resolver.caltech.edu/CaltechETD:etd-03272007-105407System Identification of Hysteretic Structures
https://resolver.caltech.edu/CaltechTHESIS:12192018-105342164
Year: 1985
DOI: 10.7907/p43n-j428
<p>This thesis is concerned with the earthquake response of hysteretic structures subjected to strong ground acceleration. Several earthquake records corresponding to different instrumented buildings are analyzed. Based on these observations, a new model for the dynamic behavior of reinforced concrete buildings is proposed. In addition, a suitable system identification algorithm to be used with this new model is introduced. This system identification algorithm is based upon matching the restoring force behavior of the structure rather than the time history of the response. As a consequence, the new algorithm exhibits significant advantages from a computational point of view. Same numerical examples using actual earthquake data are discussed.</p>https://resolver.caltech.edu/CaltechTHESIS:12192018-105342164A Model for the Rigid Body Motions of Skew Bridges
https://resolver.caltech.edu/CaltechTHESIS:02132019-102055741
Year: 1985
DOI: 10.7907/YWES-NJ36
<p>This thesis investigates the rigid body motions of skew bridges, concentrating on the in-plane translational and rotational displacements of the bridge deck induced by impact between the deck and the abutments. Experience in the San Fernando Earthquake of February 9, 1971 demonstrates that this feature is particularly important for skew bridges.</p>
<p>A simple model, in which the bridge deck is represented by a rigid rod restricted by column and abutment springs is examined first. This model illustrates the mechanism by which in-plane rotational vibrations is triggered after the closure of the gap between the bridge deck and the abutment. It also shows that the force-deflection relations of the columns and the abutments are particularly important features for the response of the bridge. Methods for the exact and approximate estimation of the elastic stiffness of elastically founded, tapered bridge columns with octagonal cross section are presented next. The methods are applied to a bridge used later as an example. In addition, the yielding of the columns is examined and the force-deflection relations for bending about two orthogonal axes are estimated.</p>
<p>The abutments are treated as rigid bodies and the soil embankments as Winkler Foundations with elastic spring constants increasing with depth. For the examination of the yielding of soil the Rankine theory is used. Based on these assumptions an approximate force deflection relation for the abutments is constructed.</p>
<p>The response of a more complicated bridge model applied to a bridge near Riverside, California is examined at the end of the thesis and examples of the results are given. This model, in which the bridge deck is still represented as a rigid rod, has three in-plane degrees of freedom: two orthogonal displacements and a rotation, and is capable of capturing many of the more important features of the nonlinear, yielding response of skew bridges during strong earthquake shaking.</p>https://resolver.caltech.edu/CaltechTHESIS:02132019-102055741Millimeter-Wave Integrated-Circuit Antenna Arrays
https://resolver.caltech.edu/CaltechETD:etd-08172005-102232
Year: 1985
DOI: 10.7907/ddxq-rj80
<p>This thesis presents three different types of millimeter-wave integrated-circuit antenna array. They are a linearly polarized antenna array that can form polarization and intensity line images, a circularly polarized spiral antenna and a two-dimensional tracking antenna array. They are all integrated-circuit antennas with detectors on quartz substrates using quasi-optical systems to collect and focus the waves.</p>
https://resolver.caltech.edu/CaltechETD:etd-08172005-102232Dynamic Response of a Partially Embedded Bar Under Transverse Excitations
https://resolver.caltech.edu/CaltechTHESIS:01222019-152401456
Year: 1985
DOI: 10.7907/pp2r-fc10
<p>This dissertation is concerned with the dynamic response of a finite flexible bar partially embedded in a half-space, under transverse loadings. The loadings are applied at the unembedded end of the bar and may, in general, be a combination of time-harmonic shear and moment. The problem is intended to serve as a fundamental idealization for the dynamic analysis of piles or other embedded foundations whose flexibilities are not negligible.</p>
<p>By treating the bar as a one-dimensional structure and the half-space as a three-dimensional elastic continuum, the interaction problem is formulated as a Fredholm integral equation of the second kind. The essential tool required in the formulation is a group of Green's functions which describe the response of an elastic half-space to a finite, distributed, buried source which acts in the lateral direction. By means of a technique developed for a class of three-dimensional asymmetric wave propagation problems, the Green's functions are derived as integral representations. A numerical procedure for the computation of the semi-infinite Hankel-type integrals involved is presented which is free of the basic difficulties commonly encountered in such problems. Owing to the special nature of the kernel function, a numerical scheme which contains the essence of quadrature and collocation techniques is developed for the solution of the governing integral equation. Selected results for the interaction problem are presented to illustrate various basic features of the solution. In addition to furnishing the compliance functions commonly used in soil-structure interaction studies, the solution should prove useful in providing a basis for the assessment and improvement of approximate and numerical models currently employed for such analyses.</p>https://resolver.caltech.edu/CaltechTHESIS:01222019-152401456Structural Analysis of Imperfect Three-Legged Truss Columns for Large Space Structures Applications
https://resolver.caltech.edu/CaltechETD:etd-11182004-161353
Year: 1985
DOI: 10.7907/YXNE-YE65
<p>Three-legged truss columns are basic structural components of many envisioned large outer-space structures. They constitute three longerons ('legs') forming, in the column cross-section, the vertices of an equiliateral triangle. Their longerons are held together by uniformly spaced battens while a shear web, usually made of diagonals, restrains shear deformation.</p>
<p>This work deals with configurations characterized by having relatively stiff battens, longerons which are pinned to the battens and prestressed string diagonals. Considered are only simply-supported slender columns having slender longeron segments and relatively thin and lightly preloaded diagonals. The columns are allowed to have global (overall) as well as local (longeron segment) geometrical imperfections - not necessarily small ones.</p>
<p>Investigated is the static structural behavior of such columns when loaded by purely axial compressive concentrated forces acting at the supports. Addressed are the topics of global and local buckling, post-buckling, imperfection sensitivity, global-local mode interaction, complete non-linear response, limit loads and diagonals slackening and post-slackening.</p>
<p>The approach is a theoretical one; a system of non-linear, ordinary differential equations is set up which represents the column, and results, mostly in closed form, are obtained by solving that system for a variety of cases of varying generality.</p>
<p>First, a highly idealized case is studied in detail, in which the diagonals are removed and infinite shear rigidity is postulated instead. The results exhibit most of the essential features of the more complicated cases. Next, the case of the undeflected or only-slightly deflected column is considered. Results include the prebuckling behavior, slackening and local buckling loads, global buckling load, initial post-buckling behavior and imperfection sensitivities. Diagonals slackening in a deflecting column is studied next. This is done by means of slackening loci constructed in the load-deflection plane. Solutions are obtained for some special cases of a deflecting column. These include a complete analysis of the locally-perfect case and the cases of small load and high defection. Also obtained is an engineering-oriented load-deflection working relation valid for the most general case but based on generalization rather than on rigorous solution. A torsion-compression mode, dominant in post-slackening, is also analyzed. The work is concluded by investigating the error committed in treating continuous longerons as if they were discontinuous-pinned.</p>
https://resolver.caltech.edu/CaltechETD:etd-11182004-161353A Simple Strain-Space Plasticity Model for Clays
https://resolver.caltech.edu/CaltechTHESIS:01022019-123640478
Year: 1985
DOI: 10.7907/kcgf-c188
<p>This thesis develops and demonstrates a simple strain-space constitutive model for wet clays. It has been seen that a strain-space formulation of the constitutive behavior of engineering materials facilitates the solution of boundary value problems involving these materials. Soil, because of its multi-phase granular constitution poses challenging problems in constitutive modeling. Although several stress-space plasticity models exist for soils, they are not used commonly in engineering practice due to their complexity. It is attempted herein to develop and test a simple model which could result in simplified solutions for some soil problems.</p>
<p>The model is based on the experimentally observed physical behavior of soil. Certain approaches alien to conventional plasticity. Are employed so that the material behavior is closely predicted without sacrificing the simplicity of the model.</p>
<p>The model is initially developed for triaxial load systems. Its predictions are then tested against other model predictions and experimental data. The model is then generalized. The generalization renders the model capable of handling general stress-strain states and finite deformations.</p>
<p>Finally, the generalized model is used to solve an idealization of a practical problem. The problem of a pile driven into a soil medium is idealized as an expanding cavity in a homogeneous infinite medium. The solution predicted by the strain-space model is compared with other model predictions and test results.</p>https://resolver.caltech.edu/CaltechTHESIS:01022019-123640478Range Dependent Signals and Maximum Entropy Methods for Underwater Acoustic Tomography
https://resolver.caltech.edu/CaltechETD:etd-04092008-080843
Year: 1985
DOI: 10.7907/hrqs-cv92
<p>A new method for simulating underwater acoustic signals in range dependent environments is presented, and the approach utilizes Maslov asymptotic theory as developed by C. H. Chapman for synthetic seismograms. The simulated range dependent signals are then used in active underwater acoustic tomography exercises, where changes in observed acoustic transmissions are inverted to obtain information about ocean sound velocity structure. The inversions are performed with both the generalized inverse and the maximum entropy inverse, and a new numerical method for finding the maximum entropy inverse with noisy data is presented. The numerical technique follows the ε statistic approach proposed by Bryan and Skilling.</p>
https://resolver.caltech.edu/CaltechETD:etd-04092008-080843Dynamic and Spectral Features of Semiconductor Lasers
https://resolver.caltech.edu/CaltechETD:etd-02082005-114440
Year: 1985
DOI: 10.7907/H7JA-K512
<p>This thesis is divided into two main subject areas: the fluctuation properties of state of the art semiconductor lasers and the improvement of modulation and fluctuation properties in these devices through a technique called detuned loading.</p>
<p>The discussion of fluctuations in lasers is a topic as old as the device itself, and much of the pioneering work in this field was done in the sixties. Surprisingly, however, several new chapters in this field are being written, because of certain pecularities only recently observed in semiconductor lasers. Chapters 2 and 3 of this thesis will consider these pecularities, which, as it turns out, are quite important in many potential system applications of these devices.</p>
<p>One of the driving forces behind the development of semiconductor lasers has been their application as sources and local oscillators in optical communication systems. In general, such applications require lasers which have low phase and intensity noise, and which can be modulated at high data rates. As is often the case, these requirements are to a certain extent mutually exclusive. Chapter 4 introduces a technique which is an exception to this rule. It relies upon the semiconductor laser physics which produces the fluctuation abnormalities discussed in Chapters 2 and 3. The technique can be used to improve modulation speed while simultaneously reducing noise as compared to the conventional device.</p>https://resolver.caltech.edu/CaltechETD:etd-02082005-114440On the Existence and Uniqueness of the Solution to the Small-Scale Nonlinear Anti-Plane Shear Crack Problem in Finite Elastostatics
https://resolver.caltech.edu/CaltechETD:etd-03212008-094413
Year: 1985
DOI: 10.7907/dfcw-j110
<p>This thesis addresses the issue of existence and uniqueness of the solution to the small-scale nonlinear anti-plane shear crack problem in finite elastostatics. The hodograph transformation, commonly used in the theory of compressible fluid flows, plays an essential role. Existence is established by exhibiting an exact closed form solution, constructed via the hodograph transformation. Uniqueness is established by first proving the uniqueness of the solution to a related boundary-value problem, which is linear by virtue of the hodograph transformation, and then examining the implications of this result on the original problem. The possibility of making some of the conditions imposed on the solution to the small-scale nonlinear crack problem less restrictive is then investigated. This leads to several further results, including estimates of the nonvanishing shear stress component of the stress tensor along the crack faces.</p>https://resolver.caltech.edu/CaltechETD:etd-03212008-094413Effects of Ambient Pressure on the Instability of a Liquid Boiling Explosively at the Superheat Limit
https://resolver.caltech.edu/CaltechETD:etd-04102008-081638
Year: 1985
DOI: 10.7907/8J3K-PS54
<p>The effect of ambient pressure on the dynamical behaviour of a single droplet (1-2 mm diameter) of volatile liquid boiling explosively at the limit of superheat is studied experimentally and theoretically. In a series of experiments it is shown that the evaporative instability, observed earlier by Shepherd & Sturtevant (1982) during the rapid vapourization of butane droplets at atmospheric pressure, is suppressed at high pressure. Three other fluids (pentane, isopentane, and ether) are tested to establish the generality of the instability and other transient processes previously observed. Direct evidence is obtained showing that during violently unstable boiling small liquid particles are torn from the liquid-vapour interface. This ejection of fine droplets from the evaporating surface produces a mass flux orders of magnitude greater than that characteristic of ordinary boiling.</p>
<p>Raising the ambient pressure lowers the superheat attained at the superheat limit, which decreases the vapourization rate. At high pressure boiling consists of normal slow vapourization from a smooth interface. Observed bubble growth rates show reasonable agreement with theory. At intermediate pressures a transitional regime of stability occurs in which a drop initially vapourizes stably for several milliseconds while incipient instability waves develop on the evaporating interface. When only a small amount of liquid remains in the drop in the shape of a thin cap, heat transfer from the surrounding hot host fluid initiates violent boiling at the edge of the liquid cap. The subsequent rapid vapourization generates a radiated pressure field two orders of magnitude larger than during stable boiling, and sets the bubble into violent oscillation. The bubble is subject to the Rayleigh-Taylor instability and rapidly disintegrates into a cloud of small bubbles.</p>
<p>Lowering the ambient pressure decreases the time delay between nucleation and onset of unstable boiling. For example, in ether at atmospheric pressure the instability is triggered less than 8 µsec after nucleation, shortly after the smooth vapour bubble contacts the droplet surface. Heterogeneous nucleation spreads out along the surface of the drop while disturbances (with a length scale of 100 µm) distort the unstably evaporating interface within the drop, substantially enhancing the vapourization rate. At early times, droplets torn from the evaporating surface evaporate before the instability-driven jet impinges upon the surrounding fluid, bulging the bubble surface. The last portion of liquid in a drop boils particularly violently and droplets ejected from the evaporating interface at this time remain intact to splatter the bubble surface. At subatmospheric pressures the most rapid vapourization occurs and temperature gradients within a drop produce spatial variations in vapourization rate.</p>
<p>The Landau mechanism for the instability of laminar flames is adapted to the case of evaporation to investigate the effects of variable ambient pressure. A spherical version of the theory, applicable before the vapour bubble contacts the droplet surface, predicts absolute stability at atmospheric pressure. At later times the spherical constraint is inappropriate and planar theory yields results in general agreement with observation. Differences in fluid properties make some fluids more prone to instability than others. The product of the maximum growth rate with the time interval the interface is predicted to be linearly unstable measures the susceptibility to instability. For practical estimates it is suggested that a value of 3 of this parameter be taken as the lower limit for instability. The sensitivity of the instability to temperature suggests that small temperature nonuniformities may be responsible for quantitative departures of the behaviour from predictions.</p>
https://resolver.caltech.edu/CaltechETD:etd-04102008-081638Thin Film Silicide Formation by Thermal Annealing: Study of Kinetics, Moving Species, Impurity Effect, and Electrical Properties
https://resolver.caltech.edu/CaltechETD:etd-03272008-074200
Year: 1985
DOI: 10.7907/t5r5-5267
<p>Growth kinetics, dominant moving species (DMS), impurity effect, and electrical properties of thermally formed silicides have been studied by using MeV<sup>4</sup>He<sup>+</sup> Rutherford backscattering spectrometry, <sup>18</sup>O(p,α)<sup>15</sup>N nuclear reaction analysis, four—point probe measurement, and I—V measurement.</p>
<p>The growth kinetics (including growth rate and activation energy of growth rate) measurements are done for silicides formed on different kinds of Si substrates, viz., single crystalline (100) Si (Si<sup>c</sup>) and amorphous evaporated Si (Si<sup>e</sup>). Results show that the substrate can have different effects on different silicides. Some silicides grow much faster on Si<sup>e</sup> than on Si<sup>c</sup> (e.g., NiSi<sub>2</sub>,CoSi<sub>2</sub>), some show the reverse phenomenon (e.g., Co<sub>2</sub>Si, CoSi), and some have similar growth rates (e.g., NiSi, Ni<sub>2</sub>Si, Pt<sub>2</sub>Si, PtSi) (see Table 2). Some silicides are more uniform and form at lower temperature on Si<sup>e</sup> than on Si<sup>c</sup> (e.g., CrSi<sub>2</sub>, NiSi<sub>2</sub>, CoSi<sub>2</sub>). These interesting phenomena are discussed and explained in terms of the different properties between the samples with either substrate (see Chapter 2).</p>
<p>When studying the formation of a silicide, one would like to know the DMS in silicide during the silicide formation. Not only is it an important property of the silicide but it is closely related to the silicide formation. The DMS is, in general, measured by inert marker experiments. In Chapter 3, we use such marker experiments to study the DMS in a silicide during silicide formation and two other silicide reactions (viz., solid-phase-epitaxy (SPE) of Si<sup>e</sup> through silicide and silicide oxidation). The reason for measuring the DMS for the two additional types of silicide reactions is that all these reactions are related and additional information can be obtained from this comparison. The results, in fact, show that in all three reactions, the DMS in the silicide is the same when the silicide formation is diffusion—controlled. An explanation is given (with some assumptions) by considering the detailed atomic motion inthe silicide during these reactions (see Chapter 3).</p>
<p>Inert marker experiments can identify the DMS in a silicide. They cannot, however, distinguish whether the DMS diffuses by an interstitial (or grain boundary) or a vacancy mechanism. One possible way to determine the diffusion mechanism of the moving species is by using tracer experiments. The problem with the tracer studies is that the measured tracer profiles can be (and have been) misinterpreted. We review several models that were used to explain the tracer profiles, point out incorrect considerations and finally give a plausible model to explain what information can be obtained from the tracer experiments (see Chapter 4).</p>
<p>During marker experiments, one may find that the marker used to monitor the DMS can affect the growth rate of silicide, and sometimes even change the DMS. This points to a general problem, namely, how foreign atoms (impurities) introduced in a sample affect the properties of silicide. Since the effect of impurity is important in our thin film reactions, we have systematically studied the effect of oxygen on the growth rates of silicide, and its redistribution, by using a rare isotope of oxygen, <sup>18</sup>O, as an impurity. The results are explained in terms of a modified model which was originally proposed by Scott (see Chapter 5).</p>
<p>Finally, we study the electrical properties of Co silicides. Co silicides formed from Si<sup>e</sup> (silicides thus formed are more uniform than that formed from Si<sup>c</sup>) are used for the measurements of Schottky barrier height, resistivity, Hall mobility, and carrier concentration. From the result of this study, we suggest that that CoSi<sub>2</sub> is a potential candidate for contacts to shallow junctions and as an interconnection material in VLSI (see Chapter 6).</p>
<p>Further works, arising out of the implications of these studies, are suggested and summarized in the last chapter of the thesis.</p>https://resolver.caltech.edu/CaltechETD:etd-03272008-074200Stochastic Analysis of the Seismic Response of Secondary Systems
https://resolver.caltech.edu/CaltechTHESIS:02012019-085357846
Year: 1985
DOI: 10.7907/w4cj-w767
<p>This thesis is concerned with the earthquake response of light equipment in structures. The motion of the ground during an earthquake is represented as a stochastic process in order to reflect uncertainty in the prediction of such motion. A number of different stochastic earthquake models are considered, and analytical methods are described for these models.</p>
<p>The response of equipment in a structure to stochastic ground motion is derived, in the case of a single-degree-of-freedom secondary system (equipment) attached to a single-degree-of-freedom structure. The distribution of the envelope of the secondary system displacement is obtained for general transient ground motion. Closed form expressions are computed for the transient response to stationary ground motion.</p>
<p>The effect of the interaction of equipment with the structure is described by the introduction of an equivalent non-interacting system. However, this method applies only to classically damped systems.</p>
<p>The results are applied in a simple way to the problem of the computation of floor spectra. It is found that the ground spectrum is amplified in a simple way, except near resonance, where special considerations must be addressed.</p>https://resolver.caltech.edu/CaltechTHESIS:02012019-085357846Ray Tracing in Complex Three-Dimensional Earth Models
https://resolver.caltech.edu/CaltechETD:etd-03182008-140018
Year: 1986
DOI: 10.7907/d9ts-vp45
<p>The problem of tracing seismic rays between specified source and receiver is discussed for Earth models consisting of layers, in which velocity varies linearly, that are separated by material interfaces of arbitrary shape. The calculation of travel times, amplitudes, and phase shifts is considered. Fast and efficient numerical algorithms are developed. Computed examples are presented.</p>https://resolver.caltech.edu/CaltechETD:etd-03182008-140018Analysis of Unanchored Liquid Storage Tanks under Seismic Loads
https://resolver.caltech.edu/CaltechTHESIS:10232019-110854163
Year: 1986
DOI: 10.7907/w43k-hj54
<p>Because of cost, cylindrical, ground supported liquid storage tanks are often not fixed to their foundation, even in seismic areas. For such an unanchored tank made of steel, the weight of the cylindrical shell is mostly insufficient to prevent local uplift due to seismic overturning moments. Although, for properly designed connecting pipes, uplift itself is not a problem, it results in larger vertical compressive stresses in the tank wall at the base, opposite to where the uplift occurs. These compressive stresses have often caused buckling, even in earthquakes which did not cause much damage to other structures.</p>
<p>Various investigators have studied the behavior of unanchored tanks experimentally, but, due to the complexity of the problem, so far very little theoretical work has been done. Two methods of analysis for static lateral loads are presented: An approximate one in which the restraining action of the base plate is modeled by nonlinear Winkler springs, and a more comprehensive one in which the two dimensional nonlinear contact problem is solved by the finite difference energy method. The theoretical results are compared with existing experimental results and with the approach from current U.S. design standards. The theoretical peak compressive stresses are in good agreement with the experimental results, but in some cases exceed those calculated by the code method by more than 100%.</p>
<p>Finally, a new design concept, by which the tank wall is preuplifted all around its circumference by inserting a ring filler is described. It will be shown theoretically and experimentally that this preuplift method substantially improves the lateral load capacity.</p>https://resolver.caltech.edu/CaltechTHESIS:10232019-110854163Some Issues in the Kinematics of Finite Deformations
https://resolver.caltech.edu/CaltechETD:etd-03212008-074451
Year: 1986
DOI: 10.7907/5rhm-hb74
<p>This dissertation deals chiefly with various issues pertaining to the existence and uniqueness of a finite deformation that gives rise to a prescribed right or left Cauchy-Green strain-tensor field.</p>
<p>Following a review and discussion of available existence and uniqueness theorems appropriate to a pre-assigned <i>right</i> strain field, the extent of uniqueness of a generating deformation is established under minimal smoothness and invertibility assumptions. Further, the compatibility equations of finite continuum kinematics are used to arrive at an analytical proof of Liouville's theorem on conformal deformations, which supplies an exhaustive classification of three-dimensional deformations that preserve all angles.</p>
<p>The remainder of the dissertation is devoted to the more involved corresponding existence and uniqueness questions for a given <i>left</i> strain-tensor field. These questions are first discussed in a three-dimensional setting and are then resolved for the special class of plane deformations. The results thus obtained stand in marked contrast to their counterparts for a given right strain field.</p>
https://resolver.caltech.edu/CaltechETD:etd-03212008-074451Modelling and Estimation of Leakage Phenomena in Magnetic Circuits
https://resolver.caltech.edu/CaltechETD:etd-03262008-111040
Year: 1986
DOI: 10.7907/VTCM-S717
<p>A new modelling method for magnetic circuits is presented in this thesis. This method can be used to model magnetic circuits with any number of windings. The models incorporate adequate information about the correct distribution of leakage energy, the presence of gaps throughout the core, the arrangement of the windings, and the type of core used.</p>
<p>These new electric circuit models (<i>physical models</i>) are "physically natural"; i.e., the elements in the models have a one-to-one relationship with corresponding physical quantities in the original magnetic structure.</p>
<p>Several commonly used arrangements such as toroids with uniformly distributed turns, and bobbin core structures with multiple windings were modelled with the new technique. The measured electric circuit model values always compared favorably with the predicted physical values derived with the new method.</p>
<p>By breaking the windings of the magnetic circuit into their separate layers, a more elaborate and accurate set of models (layer-to-layer models) can be obtained. These models incorporate additional information about the correct distribution of the windings and interwinding self-capacitances. Because of the complicated nature of these elaborate models, they are more suitable for computer analysis of magnetic circuits.</p>https://resolver.caltech.edu/CaltechETD:etd-03262008-111040Two-Phase Soil Study: A. Finite Strain Consolidation. B. Centrifuge Scaling Considerations
https://resolver.caltech.edu/CaltechETD:etd-03082008-084249
Year: 1986
DOI: 10.7907/agt3-mf84
<p>Two different aspects of the behavior of soil as a two-phase medium are studied, namely, the consolidation of soil and scaling relations for soils in centrifuge testing.</p>
<p>PART A</p>
<p>First a consistent approach is presented that unifies all current theories of consolidation of soil. For one-dimensional finite strain consolidation, a Lagrangian finite element scheme is then given and tested against three different experiments and found to give consistent results. For a quick solution to a particular problem, the regular perturbation method applied to the formulation in which the dependent variable is the natural strain is shown to give the most consistent results. For the Eulerian formulation, the material derivative contains a convective term. This convective effect is then analytically studied and found not to be negligible for a final natural strain greater than 10%. A method is then introduced that can account for both the moving boundary and the convective effect. This method is tested in a finite difference scheme and found to give identical results with the Lagrangian finite element scheme for the one-dimensional case. Finally the method is used for the axisymmetric problem of consolidation by vertical drain. The solution to this case suggests that arching and subsequent load redistribution should be considered.</p>
<p>PART B</p>
<p>Conceptually, when a centrifuge is used to test models, the centrifuge is assumed to produce an equivalent ng gravitational field (as on another planet) and the behavior of the model in the ng field is then assumed to be similar to that of the prototype. For most static problems, the centrifuge does model the prototype well but for some dynamic problems, these assumptions can break down. To investigate this, the similarity requirements are examined for the case of a single particle moving in a fluid. It is found that for the post-liquefaction process and for seepage flow, unless the Reynolds number is much less than one in both model and prototype, the centrifuge is not a good simulation of the prototype situation. But, perhaps contrary to expectations, the breakdown is due to the fact that the behavior in the ng planet is not similar to the prototype ig planet, whereas the centrifuge does simulate the ng planet well. Further, it is shown that the concept of "modeling of models" can lead to misleading results. Lastly, for cratering experiments, it is concluded that the centrifuge will only model the crater shape just after an explosion and not the final crater shape.</p>https://resolver.caltech.edu/CaltechETD:etd-03082008-084249Internal Solitons Generated by Moving Disturbances
https://resolver.caltech.edu/CaltechETD:etd-03122008-080220
Year: 1986
DOI: 10.7907/pspg-vp83
<p>A new phenomenon of the generation of internal solitons is investigated in this thesis by applying theoretical models and is observed in both numerical and experimental results. By imposing an external disturbance, such as a top surface pressure or a bottom bump, that moves with a constant velocity within a trans critical range after an impulsive start from rest, upon a two-layered or a continuously stratified fluid system, a series of solitons are generated, one after another periodically, each surging ahead of the disturbance in turn. Two theoretical models, belonging to the generalized Boussinesq class, are developed to investigate the generation of weakly nonlinear and weakly dispersive long waves and their evolution in an inviscid, immiscible, and incompressible stratified fluid system under the forcing of the external disturbances. The top surface may be either free or covered by a rigid horizontal plate. For the generalized Boussinesq class for two-layered fluid systems, we have derived the FOUR-equation model for the free top-surface case and the THREE-equation model for the rigid horizontal top-surface case; these are extensions of the one-layer homogeneous fluid system previously considered by Wu (1979). For primarily unidirectional motions a forced KdV equation is obtained which represents each normal mode of a two-layer system or a continuously stratified fluid system. Numerical schemes have been successfully developed to solve these equations. Experiments were performed to investigate this phenomenon,henomenon using fresh water to form the upper layer and brine the lower layer. The relationship between the main properties (the amplitude and the period of generation) of the generated solitons and the forcing function configurations is discussed along with comparisons of theoretical, numerical and experimental results. Qualitatively all the results are consistent in exhibiting the salient features of the resulting motion. Quantitatively the numerical results based on the continuously stratified fluid model seem to be more satisfactory than those given by the two-layered fluid model in comparison with the present experiments. The discrepancy between the theory and experiment is supposedly due to the viscous effects, which will be left for future work.</p>
https://resolver.caltech.edu/CaltechETD:etd-03122008-080220The Effect of Strain-Softening Cohesive Material on Crack Stability
https://resolver.caltech.edu/CaltechETD:etd-02242004-152909
Year: 1986
DOI: 10.7907/sqjv-pf95
<p>Part I</p>
<p>Failure mechanisms of materials under very high strains experienced at and ahead of the crack tip (such as the formation, growth and interaction of microvoids in ductile materials, microcracks in brittle solids or crazes in polymers and adhesives) are represented by one-dimensional, nonlinear stress-strain relations possessing different post-yield softening (unloading) behaviors. These reflect different ways by which the material loses capacity to carry load up to fracture. A DCB type specimen is considered in this study. The nonlinear material is confined to a thin strip between the two elastic beams loaded by a wedge. The problem is first treated as a beam on a nonlinear foundation for which the pertinent equation is solved numerically as a two-point boundary value problem for both the stationary and the quasi-statically propagating crack. A finite element model is then used to model the problem in more detail to assess the adequacy of the beam model for reduction of the experimental data.</p>
<p>It is found that the energy release rate G = 2(γb) = {3P<sup>2</sup>δ)<sup>2</sup>/EI}<sup>1/3</sup> derived by assuming the built-in conditions at the crack tip could be used to calculate the fracture (surface) energy more accurately and conveniently than the conventional scheme even in cases where the built-in assumption is invalid. Results for the deformations of the beam prior to or during crack growth suggest ways to approximately characterize the complete material stress-strain behavior, including loading and strain-softening characteristics.</p>
<p>Part II</p>
<p>This study investigates the effects of nonlinear fibril behavior on the mechanics of craze and crack growth. We developed a numerical method for determining the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement (P-V) behavior, including strain softening characteristics.</p>
<p>The problem formulation is based on the superposition of the relevant elasticity Green's function. The solution is effected by using Picard's successive approximation iterative scheme. Both field equilibrium and the Barenblatt condition for vanishing stress and strain singularities (K<sub>I</sub> = 0) are satisfied simultaneously, rendering the craze tip profile cusp-like as observed experimentally. The formulation allows the stress distribution profile and the corresponding P-V relation to be computed from experimentally measured craze/crack contours with certain advantages over the methods proposed to date.</p>
<p>Further numerical investigations indicate that only certain classes of the fibril P-V relations are consistent with realistic craze profiles, i.e., profiles with nonnegative displacements at all points. In addition, it is found that for a given P-V relation, nontrivial solutions -- the 'trivial solution' refers to the solution corresponding to a fully closed craze, i.e., zero displacements throughout or, simply: no craze exists -- exist only for certain ranges of craze lengths depending on the P-V characteristics under consideration.</p>
<p>Quasi-static growth of a craze with a central crack is analyzed for different nonlinear P-V relations for the craze fibrils. A 'critical crack tip opening displacement' (CTOD) or more precisely, 'critical fibril extension' is employed as the criterion for fracture. The P-V relation is further assumed to be invariant with respect to the craze and crack lengths. For comparison purposes, the results are compared and contrasted with the Dugdale model. The craze zone size and the energy dissipation rate are shown to approach asymptotic values in the limit of long cracks.</p>
<p>The problem of craze growth from a precut crack under increasing far-field loading is then studied. Instability is shown to occur in the case where the P-V relation is monotonically softening: The crack could start to grow unstably before the crack tip opening displacement reaches its critical value.</p>https://resolver.caltech.edu/CaltechETD:etd-02242004-152909Flow-Induced Vibration of Long Structures
https://resolver.caltech.edu/CaltechETD:etd-11072006-091025
Year: 1986
DOI: 10.7907/ZXWC-ZZ44
<p>When a body is exposed to a flowing fluid, oscillations can occur due to one or more of several different mechanisms. The resulting large amplitudes of motion and fatigue are potential sources of structural failure. Furthermore, the drag force on a structure can be increased due to the effectively larger cross-sectional area presented to the flow from the oscillation. A complete understanding of the nature of such vibration is essential in the design of many civil and mechanical engineering systems.</p>
<p>Previous solutions to the vortex-induced vibration problem were primarily based on modal analysis, using a one- or two-mode approximation. Use of modal analysis implies a "locked-in" condition: the vortex shedding frequency and a natural frequency of the system are coincident. Observations made on long cable systems indicate that the amplitude of response is smaller than is predicted by a conventional modal analysis. The drag forces on such structures are therefore overestimated by current design approaches.</p>
<p>In very long structures, typical of those found in ocean applications, modes are closely spaced, and it is not reasonable to assume total spanwise correlation in the fluid forces or response. The approach used herein attempts to avoid the limitations associated with the modal solution of such problems by implementing a solution based on traveling waves. The technique draws on earlier theoretical and empirical models for the complex vortex-shedding phenomenon, and incorporates these into a new method for analyzing the structural response problem.</p>
<p>The traveling wave approach can be used to model effectively spanwise variable flow environments by summing the calculated responses of adjacent active sections of cable. Until this method was developed, there was no suitable method available for modeling flow characteristics of this type. Modal analysis is effectively limited to systems with uniform flow over all or part of the system.</p>https://resolver.caltech.edu/CaltechETD:etd-11072006-091025The Nature of Oblique Instability Waves in Boundary Layer Transition
https://resolver.caltech.edu/CaltechETD:etd-05242007-150746
Year: 1986
DOI: 10.7907/7VG8-Y513
<p>An experimental study of both the weakly non-linear as well as the three-dimensional nature of boundary layer transition is conducted using the active surface heating technique of Liepmann et al. In the present study, this technique is extended to provide a means for controllably and repeatably introducing three-dimensional disturbances into a laminar boundary layer. A review of the surface heating technique is presented along with a discussion of some peculiarities encountered in extending this technique to three-dimensional geometries. A thorough description of the design and operation of a programmable 32-element heater array and the supporting instrumentation are given as well.</p>
<p>The heater array is first used to study the effect of weak nonlinearity on boundary layer transition. By keeping the forced disturbances as two-dimensional as possible, it is shown that the effects of weak non-linearity are relatively benign. The growth rates are seen to follow the linear theory up to perturbation amplitudes (τ'<sub>w</sub>τ̅<sub>w</sub>) of nearly twelve percent. The only deviation from the linear theory arises in the form of non-linearly generated harmonics phase-locked to the fundamental. It is concluded that although these non-linearly generated harmonics do alter the wave behavior to some extent, they are by themselves not sufficient to explain the transition from small linear oscillations to the large amplitude, broad-band, three-dimensional oscillations characteristic of a fully turbulent boundary layer.</p>
<p>The effect of three-dimensionality on boundary layer transition is then investigated through an analytical and experimental study of single oblique instability waves. This subject has remained largely unexplored, as such disturbances were generally thought to be more stable and therefore less dangerous than their two-dimensional counterparts. Through a series of experiments, however, it is shown that certain conditions exist for which oblique waves are observed to be more unstable than any two-dimensional wave. It is shown that oblique waves exhibit a non-stationary period-doubling behavior that is not seen in two-dimensional disturbances. A vortex pairing mechanism is proposed to explain this behavior, and is shown to occur in a manner consistent with the Biot-Savart law for the induced velocity field.</p>https://resolver.caltech.edu/CaltechETD:etd-05242007-150746Singularities and Phase Transitions in Elastic Solids: Numerical Studies and Stability Analysis
https://resolver.caltech.edu/CaltechETD:etd-03082008-083510
Year: 1986
DOI: 10.7907/0ytn-e775
<p>Numerical studies of the deformation near the tip of a crack are presented for a family of incompressible solids in the context of the theory of finite anti-plane shear of an elastic material. The numerical model computes the near-field and far-field solutions simultaneously, enabling observations of both small-scale and large-scale nonlinearity. The computed near-field solution is compared with a lowest-order asymptotic solution. An approximation for the <i>J</i>-integral under conditions of very large loads is discussed and compared with numerical results. The size of the region over which the lowest-order solution applies is observed.</p>
<p>Numerical solutions are presented for the same crack problem with materials for which the equilibrium equation changes in type from elliptic to hyperbolic as a result of deformation. These results show the emergence of surfaces of discontinuity in the displacement field in some cases. In other cases they show a chaotic mixture of elliptic phases near the crack tip.</p>
<p>Analysis of the stability of such coexistent phases is carried out for a specific material, the trilinear material. It is shown that the Maxwell relation, and therefore local stability, cannot in general be satisfied exactly for an arbitrary boundary value problem with this material. However, in those cases where it cannot be satisfied exactly, it may be satisfied in the sense of a limit of a certain sequence of deformations. This sequence produces a progressively chaotic pattern of two coexistent elliptic phases, as was observed numerically. The phases mix over a definite region in a given boundary value problem. This region may be computed using a constitutive relation which characterizes the mixture in the limit of the sequence.</p>https://resolver.caltech.edu/CaltechETD:etd-03082008-083510Linear and Nonlinear Acoustics with Nonuniform Entropy in Combustion Chambers
https://resolver.caltech.edu/CaltechETD:etd-03032008-105855
Year: 1987
DOI: 10.7907/ZXQ4-SA60
<p>A one-dimensional analytical model is presented for calculating the longitudinal acoustic modes of idealized "dump-type" ramjet engines. The geometry considered is the coaxial flow type with the inlet flow opening to the combustor at a simple dump plane. Since the frequencies are very low, the dominant modes are the one-dimensional longitudinal modes and allow the predictions to be extended to more complicated geometries (such as side dump combustors) with good success. A plane flame has been studied and incorporated into the combustor model where the flame is allowed to move or oscillate in the combustor. This provides three mechanisms of interaction at the flame sheet: change in mean temperature in the combustor, energy conversion at the sheet due to upstream fluctuations, and fluctuating heat release. A supersonic inlet upstream contains a shock wave in its diffuser section while the downstream exit is terminated by a choked nozzle. The linear coupling of the acoustic and entropy waves at the inlet shock, flame sheet, and exit nozzle along with acoustic admittances at the inlet and exit are combined to determine the stability of the system as well as the acoustic modes. Since the acoustic and entropy waves travel at different velocities, the geometry is a critical factor in determining stability. Typical values of the admittances will produce damped solutions when the entropy is neglected, but, as the ratio of the entropy to acoustic fluctuations is increased, the coupling can either feed acoustic energy into or out of different modes independently. This transfer of energy has a destabilizing or stabilizing effect on the acoustic modes of the system depending on the relative phases between the acoustic and entropy waves.</p>
<p>In the linear case, the entropy and acoustics are decoupled in the flow field. All linear coupling occurs at the boundary conditions. For cases where the entropy fluctuations are of the same order of magnitude as the pressure oscillations and the coupling is of comparable order, the linear stability of the acoustic field is strongly dependent upon the entropy fluctuations. The linear acoustics are predominantly governed by the boundary conditions; thus it is imperative that the entire system of inlet, combustor, and exit be considered together to determine the characteristic eigenvalues (resonant frequencies) and eigenfunctions (mode shapes). In addition, there are two modes of acoustic pressure oscillations: the classical acoustic mode and the entropy-induced mode of pressure oscillation. The nonlinear case treats the quadratic nonlinear fluid mechanic interactions in the coupling of two acoustic modes. The result is that the nonlinear acoustic-entropy interactions are much smaller than the acoustic-acoustic interactions for this case. Hence, the nonlinear acoustic field is influenced by the nonuniform entropy only by its dependence upon the linear solution which can be strongly dependent upon the entropy.</p>
<p>The energy in the acoustics of this model is controlled by the energy loss (gain) at the boundaries balanced with the energy gain (loss) at the flame front. Acoustic energy is typically lost at both the inlet and exit, but fluctuating entropy waves convecting with the mean flow velocity that impinge upon a choked nozzle generate acoustic waves that can, under the proper conditions, feed acoustic energy into the system. In addition, the Rayleigh condition for driving the system with a fluctuating heat release can also contribute to the stability of the system. The plane flame mechanism also contributes to the acoustic energy from the interaction of entropy and acoustic waves at a flame sheet. This allows a systematic study of the influence of entropy-acoustic wave interactions on the linear stability and modes of this combustor system.</p>
https://resolver.caltech.edu/CaltechETD:etd-03032008-105855Problems in Analysis, Control, and Design of Switching Inverters and Rectifiers
https://resolver.caltech.edu/CaltechETD:etd-03052008-091727
Year: 1987
DOI: 10.7907/2R9K-A588
<p>Control and analysis techniques in switched-mode inversion (dc-ac) and rectification (ac-dc) are examined in this thesis. Current programming and sliding mode control are used to provide regulation and obtain desired dynamic responses. The basic buck, boost, flyback, and buck-boost topologies are used to illustrate the different methods of control and analysis. For illustration, embodiments employ fast switching converters, but the techniques described can be applied to any general converter.</p>
<p>Different possibilities for the current programming of dc-ac inverters and ac-dc rectifiers are explored and the more practical and advantageous methods noted. Current reference programming improves the dynamic response of the converter and simplifies the design of the main regulatory loop. It also protects the switches from excessive current stresses and enables the parallel operation of many converters to support a common load. Constant frequency current reference programmed converters are, however, subject to oscillations under certain operating conditions.</p>
<p>Describing equations are used to obtain the low frequency characterization of current programmed converters. The system representation is first obtained in the stationary abc reference frame and then transformed to the rotating dq coordinate frame. In the dq coordinate system, the low frequency characterizations of all balanced, polyphase ac converter systems are represented by a set of continuous, time-invariant differential equations. The steady-state and linearized, small signal dynamic responses are then obtained in this rotating reference frame.</p>
<p>Sliding mode control is applied to inverters and rectifiers to provide regulation and ensure the stability of the system in the presence of small and large signal disturbances. This is a natural method of control for variable structure systems and enables the design of a robust controller that can provide stability and performance in the face of plant uncertainities. However, it requires that all or many of the states of the system be accessible and results in a variable switching frequency in the converter.</p>
<p>The equivalent control method is used to obtain the low frequency properties of the sliding mode system, and can also be used to obtain the low frequency models of duty ratio programmed converters. Different switching strategies can be used to provide sliding mode control, as well as to optimize responses, maximize efficiency, or minimize switching losses. Practical aspects such as hardware implementation, switch realization, and measurement techniques are also discussed.</p>https://resolver.caltech.edu/CaltechETD:etd-03052008-091727Dynamic Fracture Initiation and Propagation in Metals: Experimental Results and Techniques
https://resolver.caltech.edu/CaltechETD:etd-03052008-085910
Year: 1987
DOI: 10.7907/f3zy-j846
<p>Dynamic fracture initiation and propagation in ductile and brittle materials was studied experimentally using the optical method of caustics in conjunction with high speed photography. The drop weight impact test, previously used only for studies of fracture initiation, was adapted to study both dynamic fracture initiation and dynamic fracture propagation.</p>
<p>The results show that for a relatively brittle, quenched and tempered, high strength 4340 steel the dynamic fracture propagation toughness depends on crack tip velocity through a relation that is a material property. In addition, the effect of stress waves on the dynamic response of different specimen geometries is discussed and the micromechanisms of failure for this heat treatment of 4340 steel are investigated.</p>
<p>Extension of the optical method of caustics to applications in elastic-plastic fracture was studied with the goal of learning how to measure dynamic fracture initiation toughness in tough, ductile materials. Static experiments were performed on different specimen geometries of a ductile 4340 steel and 1018 cold rolled steel, and were compared to small scale yielding, plane stress, finite element results. Issues studied that are related to the applicability of caustics are the extent of the dominance of the plane stress HRR field, the effect of plasticity on the accuracy of caustics from the elastic region outside the plastic zone, and the extent of the crack tip region of three dimensionality.</p>
<p>The above approach to caustics in ductile materials was based on the assumption of validity of the HRR field. A novel approach to the use of caustics with ductile materials was taken that eliminates the concerns over the region of dominance of the HRR field, etc. In this approach a calibration experiment was performed relating the caustic diameter to the J integral for a particular specimen geometry under conditions of large scale yielding. This approach was successfully applied to optically measure for the first time the J integral under dynamic loading. Measurement of the J integral by means of strain gages was developed and applied to obtain J simultaneously with the caustics measurement.</p>
<p>At the same time (and on the same specimens) additional measurements were made including, load, load-point displacement, strains near the crack tip and out of plane displacements (measured with interferometry). These results are compared with excellent agreement to a three dimensional finite element simulation of the specimen.</p>https://resolver.caltech.edu/CaltechETD:etd-03052008-085910Mode I, Plane Stress Crack Initiation and Growth in Elastic-Plastic Solids: A Finite Element Analysis
https://resolver.caltech.edu/CaltechETD:etd-11062003-094350
Year: 1987
DOI: 10.7907/RG0C-WF30
<p>A detailed finite element analysis of crack initiation and stable crack extension is performed under Mode I plane stress, small-scale yielding conditions. A small strain, J<sub>2</sub> incremental plasticity theory is employed and both elastic-perfectly plastic materials and power law hardening materials are considered.</p>
<p>Some issues pertaining to the stationary plane stress crack problem, such as the range of dominance of the asymptotic stress and deformation fields and the amount of non-proportional loading near the crack tip are addressed. Special attention is devoted to the perfectly plastic idealization, by performing a separate singular finite element analysis, to clarify some details about the asymptotic fields near the stationary crack tip. The full-field numerical solution is used to simulate synthetic (optical) caustic patterns at different distances from the crack tip, which are compared with experimental observations and with asymptotic analytical results.</p>
<p>A nodal release procedure is used to simulate quasi-static crack extension. It is found that the asymptotic angular extent of the active plastic zone, surrounding the propagating crack tip, is from θ = 0 to about θ = 45° for the perfectly plastic case. The near-tip angular stress distribution within the active plastic zone is in good agreement with the variation in a centered fan, as predicted by a preliminary asymptotic analysis by Rice, for the perfectly plastic case. It is also observed that the σ<sub>rr</sub> stress component has a strong radial variation within the active plastic zone. The angular extent of active yielding around the moving tip increases with hardening, while its maximum radial extent ahead of the tip decreases. Clear evidence of an elastic unloading region following the active plastic zone is found, but no secondary (plastic) reloading along the crack flank has been numerically observed for any level of hardening.</p>
<p>The crack tip opening profile during growth is obtained for various levels of hardening. A ductile crack growth criterion is employed to investigate the nature of the J resistance curves under plane stress. Finally, the influence of hardening on the potential for stable crack growth is examined.</p>https://resolver.caltech.edu/CaltechETD:etd-11062003-094350Coupled-Inductor Magnetics in Power Electronics
https://resolver.caltech.edu/CaltechETD:etd-03112008-080918
Year: 1987
DOI: 10.7907/7T0E-2219
<p>Leakages are inseparably associated with magnetic circuits and are always thought of in three different negative ways: either you have them and you don't want them (transformers), or you don't have them but want them (to limit transformer short circuit currents), or you have them and want them, but you don't have them in the right amount (coupled-inductor magnetic structures). The methods of how to introduce the leakages at appropriate places and in just the right amounts in coupled-inductor magnetic structures are presented here, in order to optimize the performance of switching dc-to-dc converters.</p>https://resolver.caltech.edu/CaltechETD:etd-03112008-080918Failure of Slopes
https://resolver.caltech.edu/CaltechETD:etd-03012008-132659
Year: 1987
DOI: 10.7907/2C4G-6R71
<p>The dynamic mechanism of slope failure is studied both experimentally and analytically to establish the spatial and temporal process of failure initiation and propagation during collapse of a natural or man-made slope.</p>
<p>Model slopes, constructed of a brittle cemented sand material, are tested to collapse in a geotechnical centrifuge and the dynamics of failure recorded by motion picture film and mechanical detectors within the slope specimen. Shear failure is observed to initiate at the toe and propagate rapidly to the crest in the presence of crest tension cracking.</p>
<p>A finite difference approach is taken to numerically solve the plane strain slope stability problem under gravity, based on unstable material behavior. Using a Lagrangian differencing scheme in space and explicit integration in time with dynamic relaxation, the numerical method finds the equilibrium state of the slope as the large-time limit of a dynamic problem with artificial parameters. The solution predicts localized shear failure zones which initiate at the slope toe and propagate to the slope crest in the manner and geometry observed in the centrifuge tests. In so doing, the finite difference algorithm also demonstrates an apparent ability to predict shear failure mechanisms in solid continua in general.</p>
https://resolver.caltech.edu/CaltechETD:etd-03012008-132659Asymptotic Analysis of Thin Plates Under Normal Load and Horizontal Edge Thrust
https://resolver.caltech.edu/CaltechTHESIS:03212013-094948659
Year: 1987
DOI: 10.7907/DDP9-KW92
<p>We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions. </p>
<p>We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solutions approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes. </p>
<p>We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.</p>https://resolver.caltech.edu/CaltechTHESIS:03212013-094948659The Response of Stick-Slip Systems to Random Seismic Excitation
https://resolver.caltech.edu/CaltechTHESIS:04122019-165004448
Year: 1987
DOI: 10.7907/ntjg-hg45
<p>This thesis examines the response of stick-slip, or frictional, systems to harmonic and random excitation. Two frictional models are considered: constant slip force, or Coulomb, friction, and displacement dependent slip force, used to model a caster, or pivoting wheel. The response to harmonic excitation of systems exhibiting both frictional models is determined using the method of slowly varying parameters. Changes in the response amplitude of both systems caused by the addition of a linear centering mechanism are also examined.</p>
<p>The response of the system with displacement dependent slip force is examined under Gaussian mean zero white noise excitation using the generalized equivalent linearization method. It is shown that a lower bound is obtained from the Coulomb friction system's response.</p>
<p>For filtered random excitation, linearization methods are shown to predict erroneous displacement trends for the Coulomb system when the input has no spectral content at zero frequency. When the excitation is modeled as a Poisson pulse process, an approximate method exhibiting the proper displacement trends can be constructed. The method is shown to be accurate over a broad range of input parameters if overlaps in the input pulses are considered. A set of excitation parameters consistent with seismic events is then used to estimate final rms displacements as a function of coefficient of friction.</p>https://resolver.caltech.edu/CaltechTHESIS:04122019-165004448Some Observations on the Random Response of Hysteretic Systems
https://resolver.caltech.edu/CaltechTHESIS:04152019-163242410
Year: 1987
DOI: 10.7907/w5wv-5f87
<p>In this thesis, the nature of hysteretic response behavior of structures subjected to strong seismic excitation, is examined. The earthquake ground motion is modeled as a stochastic process and the dependence of the response on system and excitation parameters, is examined. Consideration is given to the drift of structural systems and its dependence on the low frequency content of the earthquake spectrum. It is shown that commonly used stochastic excitation models, are not able to accurately represent the low frequency content of the excitation. For this reason, a stochastic model obtained by filtering a modulated white noise signal through a second order linear filter is used in this thesis.</p>
<p>A new approach is followed in the analysis of the elasto-plastic system. The problem is formulated in terms of the drift, defined as the sum of yield increments associated with inelastic response. The solution scheme is based on the properties of discrete Markov process models of the yield increment process, while the yield increment statistics are expressed in terms of the probability density of the velocity and elastic component of the displacent response. Using this approach, an approximate exponential and Rayleigh distribution for the yield increment and yield duration, respectively, are established. It is suggested that, for duration of stationary seismic excitation of practical significance, the drift can be considered as Brownian motion. Based on this observation, the approximate Gaussian distribution and the linearly divergent mean square value of the process, as well as an expression for the probability distribution of the peak drift response, are obtained. The validation of these properties is done by means of a Monte Carlo simulation study of the random response of an elastoplastic system.</p>
<p>Based on this analysis, the first order probability density and first passage probabilities for the drift are calculated from the probability density of the velocity and elastic component of the response, approximately obtained by generalized equivalent linearization. It is shown that the drift response statistics are strongly dependent on the normalized characteristic frequency and strength of the excitation, while a weaker dependence on the bandwidth of excitation is noted.</p>https://resolver.caltech.edu/CaltechTHESIS:04152019-163242410Transient Gas Jets into Liquid
https://resolver.caltech.edu/CaltechETD:etd-04262004-113723
Year: 1987
DOI: 10.7907/4qp0-4x37
<p>An experimental investigation of the development of high velocity, impulsively initiated gas jets into liquid was conducted in an effort to understand some of the physical processes that occur for a jet of very light fluid into a dense ambient atmosphere. Four gases, refrigerants 12 and 22, nitrogen, and helium were injected into water at nozzle exit Mach numbers from 1.0 to 2.2.</p>
<p>The study showed that a gas jet into water develops in at least three stages: startup, transition, and global steady state. The startup is characterized by bubble growth; the growth rate is well predicted by classical bubble-growth theory. Jet transition is marked by axially directed flow, which penetrates through the startup bubble and which forms a cylindrical protrusion along the axis of symmetry. A combination of strong recirculating flow and liquid entrainment causes the startup bubble to deflate and to lift off and move downstream. In the steady state, instantaneous photographs show small-scale fluctuations of the jet boundary, but time-averaged photographs show the expected conical spreading of the steady jet; the measured spreading angles range from 18-25 degrees.</p>
<p>However, the most significant finding of this study is that under some conditions, the gas jet into liquid never reaches the global steady state. Instead, the jet boundary exhibits chugging: large nonlinear oscillations which lead to irregular collapses of the gas column followed by explosive outward bursts of gas. The unsteadiness observed is much more violent than the familiar fluctuations typical of constant-density jets. The length scale of the motion is generally on the order of several jet diameters; the time scale is on the order of the period for bubble collapse.</p>
<p>It was found that the amplitude and frequency of chugging are strongly dependent on the ratio of the liquid density to the gas density, the jet Mach number, and the operating pressure ratio. The conditions under which unsteadiness occurs were determined experimentally. In particular, a quantitative measure of jet susceptibility to unsteadiness has been established. Steady jets can be achieved in two ways: by being discharged from deLaval nozzles (increasing the exit Mach number) or by being overpressured.</p>
<p>The unsteady behavior is modeled as the collapse of a bubble in liquid; comparisons of collapse times show good agreement. A mechanism for the unsteadiness is discussed. It is proposed that the chugging is the response of the jet boundary to a pressure difference between the jet and surrounding liquid, which arises as the result of the rapid expansion of a light fluid into a dense ambient atmosphere. The flow is shown to be similar to the discharge of a gas from a nozzle into a channel of larger cross section. An upper limit to the pressure difference is determined based on estimates of the minimum base pressure for such channel flows; a lower limit is established for the collapse time. All experimental values are within the bounds. The derived values indicate that the pressure differences between the jet and liquid may be more than 90 percent of the ambient pressure.</p>https://resolver.caltech.edu/CaltechETD:etd-04262004-113723Entrainment, Chemistry, and Structure of Fire Plumes
https://resolver.caltech.edu/CaltechETD:etd-05052006-075204
Year: 1987
DOI: 10.7907/jazd-8n24
<p>In Part 1, the entrainment in the lowest regions of buoyant fire plumes burning from an environment of quiescent fresh air (lower layer) across an interface into an environment of hot combustion products (upper layer) is investigated. Measurements using 20 to 200 kW natural gas flames formed above a 0.19 m diameter burner show that the entrained mass flux is nearly linear with distance from the fire source and essentially independent of the fuel flow rate. Comparison with previous results suggests that this linear dependence is valid over a wide range of conditions, but that the magnitude of the entrainment near the burner is influenced by the initial buoyancy of the plume.</p>
<p>The chemistry of the products in the upper layer is also investigated. Over the ranges studied, the composition was a function of the upper-layer equivalence ratio only, and independent of the temperature of the upper layer or the residence time of the gas in it. For fuel-lean fires the product composition suggests that the fuel reaction is nearly complete, in contrast to fuel-rich fires where some of the stable intermediates are found to "freeze out" of the reaction prior to completion.</p>
<p>The experimental method is extended to entrainment measurements on steady, axisymmetric, fully turbulent jet diffusion flames of hydrogen in air. In the momentum-dominated regions of the flame, the nondimensional mass flux used to characterize this regime is found to be constant as expected. The transition between momentum-dominated and buoyancy-dominated regions is also observed.</p>
<p>In Part 2, a novel diagnostic technique, which makes use of laser light scattered by soot particles, was used in an effort to identify flame sheets within a natural gas diffusion flame. Soot particles, inherently created and consumed in the flame, were used as the scattering medium, which obviated the need for externally supplied seed material. Since no foreign material was added to the flame, the current technique can be considered truly nonintrusive. The soot distribution within a large buoyant natural gas diffusion flame is argued to be a reasonable marker for the presence of a diffusion flame. Measurements made in 47.4 to 190 kW natural gas flames stabilized on a 0.5 m diameter burner show that when soot is present within the outer boundary of the flame, it is observed as thin sheets, which become narrower in regions where the average strain rate is estimated to be greater. The structure of the soot distribution suggests that the combustion occurs along sheets of diffusion flamelets that are highly wrinkled and convoluted. Furthermore, they are distributed fairly uniformly within the volume of the flame, based on images of the associated soot, and occupy about 40 to 60% of the volume.</p>https://resolver.caltech.edu/CaltechETD:etd-05052006-075204Steady-State and Transient Methods for Modeling Chemical Reactions on Supported Catalysts
https://resolver.caltech.edu/CaltechETD:etd-06142006-131434
Year: 1987
DOI: 10.7907/x3zp-aa54
<p>A systematic experimental strategy based on fluid-phase measurements is proposed for modeling dynamic behavior of heterogeneous catalytic reactions. The strategy utilizes steady-state rate, step-response, cycled-feedstream, and feedback-induced bifurcation techniques. Ethylene hydrogenation on Pt/Al<sub>2</sub>O<sub>3</sub> was studied using this strategy. In addition, transmission infrared spectroscopy is applied to investigate support effects which accompany ethylene hydrogenation on Pt/Al<sub>2</sub>O<sub>3</sub>, and to the detailed study of CO adsorption, desorption and oxidation on Rh/Al<sub>2</sub>O<sub>3</sub>. The proposed experimental strategy combined with surface infrared spectroscopy provides a very powerful means for identification and validation of dynamic kinetic models.</p>
<p>Observed bifurcation behavior can be accurately attributed to a model for the catalytic reaction only if each dynamic element in the closed-loop experimental hardware is properly accounted for. Accordingly, time delay and feedback gain were the manipulated parameters in a feedback-induced bifurcation scheme aimed at validating a dynamic model for an experimental gas-phase reactor flow system without reaction. The apparatus consists of an isothermal, stirred, fixed-bed reactor, mass flow controllers, an infrared gas analysis system, and a computerized data acquisition and control system. Experimental bifurcations to sustained oscillations show that the stability of the reactor system is strongly influenced by delay. The relationships of time delay to Hopf bifurcation gains and frequencies provide a very sensitive basis for model comparisons.</p>
<p>Steady-state, step-response, feedback-induced Hopf bifurcation and forced concentration cycling experiments were applied to study ethylene hydrogenation over 0.05% Pt/Al<sub>2</sub>O<sub>3</sub> at 80°C. Step-response experiments indicate a time scale of 5000 s which is associated with chemisorbed hydrogen. Conversely, feedback-induced Hopf bifurcation data indicate this time scale to be on the order of 1 s in magnitude. In the overall strategy of dynamic modeling, the two techniques are complementary since each inherently focuses on an opposite region in the spectrum of time scales for the reactor system. Cycling the feedstream composition resulted in improvement of the time-average reaction rate for the ethylene hydrogenation reaction compared to steady-state reactor operation.</p>
<p>Steady-state, step-response and Hopf bifurcation data are also presented for 0.5% Pt/Al<sub>2</sub>O<sub>3</sub> at 30°C and compared with results for the 0.05% Pt/Al<sub>2</sub>O<sub>3</sub> catalyst. A single value of 2.5 s for the surface time constant associated with chemisorbed hydrogen is sufficient for modeling behavior on 0.5% Pt/Al<sub>2</sub>O<sub>3</sub>, whereas the lower-loaded 0.05% Pt/Al<sub>2</sub>O<sub>3</sub> catalyst requires two very different values. In addition, the 0.5% catalyst was used to demonstrate the general result that small discrepancies between the actual and chosen reference steady state give rise to imperfect, cusp-like bifurcations. Steady-state bifurcation data are also shown to be useful for discriminating among rival kinetic models.</p>
<p>Ethylene hydrogenation on spillover-activated alumina is proposed as an explanation for the very slow transient behavior observed for 0.05% Pt/Al<sub>2</sub>O<sub>3</sub>. Transmission infrared spectroscopy was used to study hydrogen spillover dynamics on 0.05% Pt/Al<sub>2</sub>O<sub>3</sub> at 80°C via hydroxyl/deuteroxyl exchange. Ethylene in the gas-phase markedly slows the rate of spillover. The presence of ethylene likely reduces the concentration of platinum-adsorbed hydrogen adatoms, the precursors of hydrogen spilled onto alumina, due to catalytic hydrogenation on the platinum. Surface transport of hydrogen atoms on spillover-activated alumina is proposed as an explanation for the very slow transient behavior observed for ethylene hydrogenation on 0.05% Pt/Al<sub>2</sub>O<sub>3</sub>. Infrared spectra exhibit characteristics of both hydroxyl and deuteroxyl groups for reactor feed containing only D<sub>2</sub> and C<sub>2</sub>H<sub>4</sub>. This observation confirms the existence of a dissociative ethylene adsorption process.</p>
<p>A section of the thesis unrelated to ethylene hydrogenation investigates modeling applications of transmission infrared spectoscopy (TIR) by applying it to study adsorbed CO on Rh/Al<sub>2</sub>O<sub>3</sub> during CO chemisorption, steady-state, step-response, and forced-cycling oxidation experiments at 900 torr. At 300°C, the catalyst initially supported primarily a dicarbonyl CO species, but after use exhibited spectra characteristic of a surface mostly covered by linearly bound CO. A model that describes transient, diffusion-influenced CO adsorption and desorption for the supported catalyst is presented. It suggests that the CO desorption energy depends linearly on coverage, and that the magnitude of this dependence is a function of temperature. Observed rate dependence on bulk CO concentration for O<sub>2</sub> effluent levels of 0.5% and 0.25% is interpreted considering the effects of internal and external mass transport at 300°C. Step-response and forced-cycling oxidation experiments across stoichiometric conditions exhibit oxygen and CO storage effects characteristic of CO oxidation catalysts. Data indicating autonomous oscillation of CO coverage and CO<sub>2</sub> production are also presented.</p>https://resolver.caltech.edu/CaltechETD:etd-06142006-131434Modeling and Identification in Structural Dynamics
https://resolver.caltech.edu/CaltechTHESIS:02272019-105053083
Year: 1987
DOI: 10.7907/1wwx-ca82
<p>Analytical modeling of structures subjected to ground motions is an important aspect of fully dynamic earthquake-resistant design. In general, linear models are only sufficient to represent structural responses resulting from earthquake motions of small amplitudes. However, the response of structures during strong ground motions is highly nonlinear and hysteretic.</p>
<p>System identification 1s an effective tool for developing analytical models from experimental data. Testing of full-scale prototype structures remains the most realistic and reliable source of inelastic seismic response data. Pseudo-dynamic testing is a recently developed quasi-static procedure for subjecting full-scale structures to simulated earthquake response. The present study deals with structural modeling and the determination of optimal linear and nonlinear models by applying system identification techniques to elastic and inelastic pseudo-dynamic data from a full-scale, six-story steel structure.</p>
<p>It is shown that the feedback of experimental errors during the pseudo-dynamic tests significantly affected the higher modes and led to an effective negative damping for the third mode. The contributions of these errors are accounted for and the small-amplitude modal properties of the test structure are determined. These properties are in agreement with the values obtained from a shaking table test of a 0.3 scale model.</p>
<p>The nonlinear hysteretic behavior of the structure during strong ground motions is represented by a general class of Masing models. A simple model belonging to this class is chosen. with parameters which can be estimated theoretically, thereby making this type of model potentially useful during the design stages. The above model is identified from the experimental data and then its prediction capability and application in seismic design and analysis are examined.</p>https://resolver.caltech.edu/CaltechTHESIS:02272019-105053083The Creeping Motion of Immiscible Drops Through a Converging/Diverging Tube: I. Non-Newtonian Effects of Viscoelastic Drops. II. Effects of Constant Pressure Gradient Condition for the Flow. III. Motion of Drops Through a Parallel Channel
https://resolver.caltech.edu/CaltechETD:etd-10312007-093206
Year: 1988
DOI: 10.7907/1944-bp37
<p>Experimental results are presented for the motion of neutrally buoyant drops of non-Newtonian fluid through a wavy wall tube within a Newtonian suspending fluid. The motion of these drops exhibits very different behavior with respect to both Newtonian drop-Newtonian suspending fluid system and Newtonian drop-viscoelastic suspending fluid system. In particular, drop breakup behavior is strongly modified. At small flow rates (small capillary numbers) viscoelastic drops undergo drop breakup. At large flow rates (large capillary numbers) breakup phenomena do not occur and axial drop elongation is inhibited. For the cases in which drop breakup occurs, it produces important effects on the time-dependent response of the extra pressure drop and on the drop mobility. For high polymer concentration (1%) in the viscoelastic drop, the resulting elastic effects are overshadowed by the increase in viscosity which accompanies the addition of polymer.</p>
<p>The effects of flow type on the dynamics of the drop motion in a wavy wall tube are investigated. According to the nature of the driving mechanism there are two types of flow, each one of them presenting different properties (though identical for non-drop conditions). One flow is susceptible to changes in flow resistance that may appear in the experimental setup, the other is such that the volumetric flow rate is constant. The former is generated by imposing a constant pressure gradient (CPG conditions), the latter is generated by a gear pump (CFR conditions). Drop deformation in a CPG experiment is less severe than it is in a CFR experiment. Also, under CPG conditions, the axial elongation and the mobility of a moving drop are independent of the viscosity ratio, whereas under CFR conditions they depend on it. In addition, the magnitude of the extra pressure drop caused by the passage of the drop through the test section is smaller under CPG conditions than it is under CFR conditions.</p>
<p>Finally, a more realistic simulation of flow dynamics in porous media is considered. For this purpose, a parallel channel device was tested under constant pressure gradient conditions. Measurements were taken in both arms of this device for the extra pressure drop caused by the passage of drops through one of the channels (a wavy wall tube). The ratio of the mean value of such measurements is nearly constant regardless of the value of the total volumetric flow, drop size or viscosity ratio. Obviously, the pressure drop measured in the bypass tube is a tangible indication of the increase (or decrease) in the volumetric flow through it, due to the motion of the drop through the other arm of the experimental apparatus.</p>
https://resolver.caltech.edu/CaltechETD:etd-10312007-093206Plastic Buckling of Cylinders Under Biaxial Loading
https://resolver.caltech.edu/CaltechETD:etd-11212007-083506
Year: 1988
DOI: 10.7907/ycv3-kp17
<p>An experimental investigation is carried out to study the effects of nonproportional loading in the plastic range on a buckling load. The discrepancy between experimental and theoretical results points to some principal shortcoming in the analysis. The problem has been simplified by applying axial tensile load and external press to simple cylindrical shell specimen and observing the buckling load for various nonproportional load-paths. Results are compared to numerical predictions (BOSOR5) using classical type plasticity models such as J₂ deformation and J₂ incremental theory. Significant discrepancy was found an attributed to inadequate modeling of the nonlinear material behavior. The effects of geometrical imperfections and large deflections were found to insignificant, thereby leading to an idea <u>how much</u> of the discrepancy between test and theory is due to a use of inadequate plastic model. The introduction of the Southwell plot into elastic shell buckling problem reduced the already minor effects of geometric imperfections.</p>
<p>The Christoffersen-Hutchinson corner theory model was introduced into BOSAR5 in its simplest form as presented by Poh-Sang Lam. Results obtained with this model, which allows corners to form on an initially smooth yield surface, displayed better agreement with experimental data. However, increased computational time and problems related to abrupt changes in load-path at the corner are a major concern at this present time.</p>
https://resolver.caltech.edu/CaltechETD:etd-11212007-083506A Numerical Evaluation of the Method of Equivalent Nonlinearization
https://resolver.caltech.edu/CaltechETD:etd-11082007-084824
Year: 1988
DOI: 10.7907/31g4-p045
<p>The Method of Equivalent Nonlinearization, an approach for determining the approximate steady-state probability density function for the random response of nonlinear systems, is evaluated based on numerical simulations.</p>
<p>The approach is a natural extension of the well-known Method of Equivalent Linearization, and is based on approximating the original nonlinear system by an equivalent nonlinear system. As such, the approach relies on the existence of exact solutions for the steady-state probability density function of nonlinear systems.</p>
<p>The approach is applied to a class of systems with nonlinear damping, for which there are no exact solutions. The results show an excellent agreement between simulated and predicted probability density functions for displacement, velocity and energy-based envelope. Several examples were solved, including the case of (velocity)<sup>m</sup>-damping and the Van der Pol equation.</p>
https://resolver.caltech.edu/CaltechETD:etd-11082007-084824Nonlinear Seismic Analysis of Arch Dams
https://resolver.caltech.edu/CaltechETD:etd-06112008-155515
Year: 1988
DOI: 10.7907/DJ4P-9393
<p>A nonlinear finite element procedure for arch dams is described in which the gradual opening and closing of vertical contraction joints and predetermined horizontal cracking planes are considered. A special joint element approximately represents the deformations due to plane sections not remaining plane at each open joint and allows a single shell element discretization in the thickness direction to be used for the dam. Compressive and sliding nonlinearities are not included. Finite element treatments are also used for the water, assumed incompressible, and for the foundation rock, assumed massless, with all degrees of freedom (dof) off the dam condensed out. For efficiency in the computations, the condensed water and foundation matrices are localized in a way which maintains good accuracy. The response of Pacoima Dam to the 1971 San Fernando ground motion recorded on a ridge over one abutment and scaled by two-thirds is computed first for water at the intermediate level that existed during the 1971 earthquake and then for full reservoir. In the first analysis, the dam exhibits pronounced opening and separation of the contraction joints, allowing violation of the no-slip assumption. The presence of a full reservoir greatly increases the dam response, enough to bring some of the assumptions of the analysis into question. Reducing the ground motion scale to 0.44 with full reservoir drops the response back to a reasonable level, but the contraction joint separations remain.</p>
https://resolver.caltech.edu/CaltechETD:etd-06112008-155515Compression Failure of Fibrous Laminated Composites in the Presence of Stress Gradients: Experiment and Analysis
https://resolver.caltech.edu/CaltechETD:etd-11062003-092741
Year: 1988
DOI: 10.7907/PP86-PE50
<p>A series of experiments were performed to determine the mechanism of failure in compressively loaded laminated plates in the presence of stress gradients generated by a circular cutout. Real time holographic interferometry and in-situ photomicrography of the hole surface, were used to observe the progression of failure.</p>
<p>The test specimens are multi-layered composite flat plates, which are loaded in compression. The plates are made of two material systems, T300/BP907 and IM7/8551-7. Two different lay-ups of T300/BP907 and four different lay-ups of IM7/8551-7 are investigated.</p>
<p>The load on the specimen is slowly increased and a series of interferograms are produced during the load cycle. These interferograms are video-recorded. The results obtained from the interferograms and photo-micrographs are substantiated by sectioning studies and ultrasonic C-scanning of some specimens which are unloaded prior to catastrophic failure, but beyond failure initiation. This is made possible by the servo-controlled loading mechanism that regulates the load application and offers the flexibility of unloading a specimen at any given instance in the loadtime history.</p>
<p>An underlying objective of the present investigation is the identification of the physics of the failure initiation process. This required testing specimens with different stacking sequences, for a fixed hole diameter, so that consistent trends in the failure process could be identified.</p>
<p>It is revealed that the failure is initiated as a localized instability in the 0° plies at the hole surface, approximately at right angles to the loading direction. This instability emanating at the hole edge and propagating into the interior of the specimen within the 0° plies is found to be fiber microbuckling. The microbuckling is found to occur at a local strain level of ≃ 8600 µstrain at the hole edge for the IM material system. This initial failure renders a narrow zone of fibers within the 0° plies to loose structural integrity. Subsequent to the 0°-ply failure, extensive delamination cracking is observed with increasing load. The through thickness location of these delaminations is found to depend on the position of the 0° plies.</p>
<p>The delaminated portions spread to the undamaged areas of the laminate by a combination of delamination buckling and growth, the buckling further enhancing the growth. When the delaminated area reaches a critical size, about 75-100% of the hole radius in extent, an accelerated growth rate of the delaminated portions is observed. The culmination of this last event is the complete loss of flexural stiffness of each of the delaminated portions leading to catastrophic failure of the plate. The levels of applied load and the rate at which these events occur depend on the plate stacking sequence.</p>
<p>A simple mechanical model is presented for the microbuckling problem. This model addresses the buckling instability of a semi-infinte layered half-plane alternatingly stacked with fibers and matrix, loaded parallel to the surface of the half-plane. The fibers are modelled using Bernoulli-Navier beam theory, and the matrix is assumed to be a linearly elastic foundation. The predicted buckling strains are found to overestimate the experimental result. However, the dependence of the buckling strain on parameters such as the fiber volume fraction, ratio of Youngs moduli of the constituents and Poisson's ratio of the matrix are obtained from the analysis. It is seen that a high fiber volume fraction, increased matrix stiffness, and perfect bonding between fiber and matrix are desirable properties for increasing the compressive strength.</p>https://resolver.caltech.edu/CaltechETD:etd-11062003-092741Generalized Modal Identification of Linear and Nonlinear Dynamic Systems
https://resolver.caltech.edu/CaltechTHESIS:03132013-163747278
Year: 1988
DOI: 10.7907/e70y-gz66
<p>This dissertation is concerned with the problem of determining the dynamic characteristics of complicated engineering systems and structures from the measurements made during dynamic tests or natural excitations. Particular attention is given to the identification and modeling of the behavior of structural dynamic systems in the nonlinear hysteretic response regime. Once a model for the system has been identified, it is intended to use this model to assess the condition of the system and to predict the response to future excitations.</p>
<p>A new identification methodology based upon a generalization of the method of modal identification for multi-degree-of-freedom dynaimcal systems subjected to base motion is developed. The situation considered herein is that in which only the base input and the response of a small number of degrees-of-freedom of the system are measured. In this method, called the generalized modal identification method, the response is separated into "modes" which are analogous to those of a linear system. Both parametric and nonparametric models can be employed to extract the unknown nature, hysteretic or nonhysteretic, of the generalized restoring force for each mode.</p>
<p>In this study, a simple four-term nonparametric model is used first to provide a nonhysteretic estimate of the nonlinear stiffness and energy dissipation behavior. To extract the hysteretic nature of nonlinear systems, a two-parameter distributed element model is then employed. This model exploits the results of the nonparametric identification as an initial estimate for the model parameters. This approach greatly improves the convergence of the subsequent optimization process.</p>
<p>The capability of the new method is verified using simulated response data from a three-degree-of-freedom system. The new method is also applied to the analysis of response data obtained from the U.S.-Japan cooperative pseudo-dynamic test of a full-scale six-story steel-frame structure.</p>
<p>The new system identification method described has been found to be both accurate and computationally efficient. It is believed that it will provide a useful tool for the analysis of structural response data.</p>https://resolver.caltech.edu/CaltechTHESIS:03132013-163747278On the Collapse of Long Thick-Walled Circular Tubes under Biaxial Loading
https://resolver.caltech.edu/CaltechETD:etd-11062007-080516
Year: 1988
DOI: 10.7907/VPAC-QV51
<p>The collapse phenomenon of long, thick-walled tubes subjected to axial tension and external pressure is investigated. A combined experimental and analytic approach is adopted. The diameter to thickness ratio (DA) of the tubes studied is in the range 10-40.</p>
<p>A series of collapse tests are conducted using thick-walled, small diameter tubes of two different materials. Careful measurements of geometrical and material parameters are carried out before each collapse test. Tension-Pressure collapse envelopes are obtained for tubes of different D/t and loading paths. Collapse tests involving initially ovalized tubes are also carried out. The results show that collapse strength is strongly influenced by initial ovality.</p>
<p>A two-dimensional model is used for predicting the collapse strength. The limit point behavior of a long tube with initial geometric imperfections has been modeled. The tube is assumed to be under generalized plane strain conditions and the possible variations of material and geometric parameters along the length are not considered. Hill's anisotropic plasticity theory involving a quadratic yield function is used to model the anisotropies in yield shown by drawn tubes. A power law creep model is employed to assess the effect of primary creep on collapse strength.</p>
<p>The interaction between collapse pressure and tension is found to depend on both material and geometric parameters. The yield behavior of the tube material strongly affects the collapse phenomenon. Initial ovality of the tube is shown to be a very important geometric parameter that influences collapse strength. The effect of primary creep on collapse is shown to be not very significant, for the type of materials used (304 stainless steel and 6061-O aluminum).</p>
https://resolver.caltech.edu/CaltechETD:etd-11062007-080516On the Domain of Dominance of the Asymptotic Elastodynamic Crack-Tip Fields
https://resolver.caltech.edu/CaltechETD:etd-10292003-134326
Year: 1989
DOI: 10.7907/cfz9-nk80
<p>A substantial part of the experimental data in dynamic fracture mechanics has been obtained under the assumption that the two-dimensional asymptotic elastodynamic stress-intensity factor field (the K<sup>d</sup><sub>I</sub>-field) is dominant over at least the region around the crack-tip over which the experimental measurements are made. The validity of this assumption is investigated in this thesis both experimentally and through finite-element simulations of the experiments.</p>
<p>The experiments reported in this work were on 4340 steel, three-point bend specimens loaded dynamically using a drop-weight tower. The two cases of dynamically loaded stationary cracks and dynamically propagating cracks were considered. An optical configuration is proposed that leads to a <i>bifocal</i> high-speed camera capable of focusing on two different planes simultaneously. This was used in conjunction with the method of caustics to measure the apparent stress-intensity factor simultaneously from two different regions (initial-curves) around the crack-tip. If the initial-curves lie within the domain of dominance of the asymptotic field, the measured values of the dynamic stress-intensity factor must agree to within experimental error. By suitably adjusting the optical set-up, a range of initial-curves was scanned in an attempt to map the domain of dominance of the K<sup>d</sup><sub>I</sub>-field.</p>
<p>The impact hammer and supports of the drop-weight loading device were instrumented in order to monitor the time dependent loads acting on the specimen. These loads were subsequently used as boundary tractions in dynamic two- and three-dimensional finite-element simulations of the experiments. The simulations were carried only up to the point of crack initiation. Comparison of the numerical simulations with the experimental results help in identifying the role of three-dimensionality and transient conditions on the measured stress-intensity factor values.</p>
<p>On the basis of both the experimental results as well as the numerical simulations, no sizeable annulus of dominance for the asymptotic elastodynamic field was found for the laboratory situation studied. It appears that the assumption of an underlying K<sup>d</sup><sub>I</sub>-dominant (or two-dimensional) field might not hold to a level of accuracy that would warrant many of the conclusions made in the literature regarding the crack-initiation toughness values as well as the uniqueness of the dynamic fracture toughness - crack velocity relation or its specimen and acceleration dependence.</p>https://resolver.caltech.edu/CaltechETD:etd-10292003-134326Effect of Nonuniform Seismic Input on Arch Dams
https://resolver.caltech.edu/CaltechTHESIS:06042013-091930444
Year: 1989
DOI: 10.7907/zbd0-ty45
<p>Standard earthquake analyses of civil engineering structures use uniform ground motions even though considerable variations in both amplitude and phase can occur along the foundation interface for long-span bridges and large dams. The objective of this thesis is to quantify the effect that these nonuniformities have on the structural response.</p>
<p>The nonuniform, free-field motions of the foundation interface are assumed to be caused by incident plane body waves. The medium in which these waves travel is a linear, elastic half-space containing a canyon of uniform cross section in which the structure is placed. The solutions for the free-field motions that are due to incident SH, P and SV waves are calculated using the boundary element method.</p>
<p>An analysis of Pacoima (arch) dam located near Los Angeles, California, is performed for both uniform and nonuniform excitations. The important effect of nonuniformities in the free-field motions, sometimes leading to a decrease in the dam response and sometimes to an increase, is quantified.</p>https://resolver.caltech.edu/CaltechTHESIS:06042013-091930444Experimental Studies of High-Speed Dense Dusty Gases
https://resolver.caltech.edu/CaltechETD:etd-08312006-130447
Year: 1989
DOI: 10.7907/5B1B-AY62
<p>An experimental study of the flow of high-speed dense dusty gases has been conducted in a novel shock tube facility. The flow is generated through rapid depressurization and subsequent fluidization of a stationary packed bed of particles loaded under pressure in the vertical driver section of the shock tube. The flow was studied with high-speed photography and fast-response pressure transducers.</p>
<p>The studies have been exploratory in nature. The entire process of lofting and disassembly of packed particle beds has been documented. A wide spectrum of dusty flows with particle loadings ranging from that of a fully packed plug to that of a dilute disperse particle flow was observed in this facility. Only extreme flow fields like packed plug flows and very dilute disperse particle flows were found to be uniform. All other flow fields, with intermediate particle loadings, were characterized by the simultaneous presence of dense filamentary structures and dilute dispersions of particles. Typically, while operating with 0.5 mm glass beads, flows reached speeds of 60 meters per second in a period of 25 milliseconds.</p>
<p>Two lofting configurations of the packed beds were set up. In the first configuration, the rapid depressurization of the interstitial bed fluid and the consequent initiation of bed expansion was examined. Bed expansion starts along horizontal fractures that partition the bed into slabs. While the bed is accelerating, particles rain down from the bottom surfaces of the slabs partitioning the fractures into bubbles with a characteristic honeycomb pattern. The bubbles eventually compete and the dominant ones prevail. The observed instability of the bottom surfaces of the slabs is analogous to the Rayleigh-Taylor instability observed in continuous media. The flow development in this configuration was not influenced by any wall effects.</p>
<p>The second lofting configuration is a high-speed fluidization configuration. Here, the role of the fluid entering from below the bed, in continuing the bed expansion initiated by the rapid depressurization of the interstitial bed fluid, was examined. The bed expansion occurs along expanding and elongating bubbles and the bubble walls are stretched into dense filamentary structures. Beds initially stacked with a gradient in particle size or density or both showed drastic differences in response to fluidization. The morphology of the expanded flow field in all cases was essentially the same: nonuniform, interspersed with dense filamentary structures and dilute dispersions of particles.</p>
<p>In the second lofting configuration, only the late stages of flow development were influenced by wall effects. Wall effects manifest as faster moving fluid along the walls and denser accumulation of flow structures towards the center of the channel. The bottom of the dusty flow is characterized by the presence of a <i>tail</i>; a concentric dense particle column formed by the accumulation of particles, initially present in the bottom regions of the flow. The tail terminates in a bulbous and streamlined bottom from which particles are slowly eroded by the coflowing fluid.</p>
<p>A multi-transducer probe was installed in the dusty gas flow for making dynamic pressure measurements and for correlating observations with those made through extensive flow visualization.</p>https://resolver.caltech.edu/CaltechETD:etd-08312006-130447Ellipticity and Deformations with Discontinous Gradients in Finite Elastostatics
https://resolver.caltech.edu/CaltechETD:etd-02122007-094508
Year: 1989
DOI: 10.7907/jn2t-m109
<p>Loss of ellipticity of the equilibrium equations of finite elastostatics is closely related to the possible emergence of elastostatic shocks, i.e., deformations with discontinuous gradients. In certain situations where constitutive response functions are essentially one-dimentional, such as anti-plane shear or bar theories, strong ellipticity is closely related to convexity of the elastic potential and invertibility of certain constitutive response functions.</p>
<p>The present work addresses the analogous issues within the context of three dimensional elastostatics of compressible but not necessarily isotropic hyperelastic materials. A certain direction-dependent resolution of the deformation gradient is introduced and its existence and uniqueness for a given direction are established. The elastic potential is expressed as a function of kinematic variables arising from this resolution. Strong ellipticity is shown to be equivalent to the positive definiteness of the Hessian matrix of this function, thus sufficing for its strict convexity. The underlying variables are interpretable physically as simple shears and extensions. Their work-conjugates define a traction response mapping. It is shown that discontinuous deformation gradients are sustainable if and only if this mapping fails to be invertible. This result is explicit, in the sense that it characterizes the set of all possible piecewise homogeneous deformations given the elastic potential function.</p>https://resolver.caltech.edu/CaltechETD:etd-02122007-094508Soil Stress Field Around Driven Piles
https://resolver.caltech.edu/CaltechETD:etd-02212007-130942
Year: 1990
DOI: 10.7907/GGE1-GC92
<p>The description, equipment, and results of a series of pile-driving experiments conducted in a centrifuge using a model pile driven in dry sand are presented.</p>
<p>The work was conceived on the basis of the modelling of a soil-structure system under an artificially generated gravitational field, and motivated by the need for experimental data for a better understanding of the complex phenomena involved in the pile-soil interaction during driving. The behavior of the pile itself has been the focus of more attention in the past, but few full-scale or model experimental results have been obtained to the present concerning the soil stress field during pile driving. These are necessary for comparison with analytical and theoretical work. The work presented here appears to be the first attempt to obtain dynamic response of the soil during driving. The objective was to obtain a good understanding of the physical phenomena occurring in the soil and pile during driving.</p>
<p>In order to achieve these objectives both dynamic (transient) and static responses of the soil and pile were measured by means of transducers: accelerometers and strain gages for the pile, pressure transducers for the soil. In particular, the relations between static and dynamic data were explored, which resulted in the modelling of the soil-transducer interaction with a non-linear, history-dependent, model.</p>
<p>Results were obtained regarding pile dynamics, soil dynamics, and soil stress field (radial and vertical distribution, stress contours). Both linear and soil-cell model assumptions were used, which enabled a comparison between the two, leading to an estimate that each constitutes a bound of the real stress field, with the linear giving the higher, and the non-linear the lower bound, and the true stress being closer to the lower bound.</p>
<p>The soil response during driving is obtained, filling the gap in the study of the pile-soil system, where only the pile response was known. Recommendations for further work and better experimental procedures are given.</p>https://resolver.caltech.edu/CaltechETD:etd-02212007-130942Time-Temperature Response of Multi-Phase Viscoelastic Solids Through Numerical Analysis
https://resolver.caltech.edu/CaltechETD:etd-10292003-112909
Year: 1990
DOI: 10.7907/SYAS-2A50
<p>A numerical model has been constructed for the study of the properties of multi-phase viscoelastic composites. The model utilizes the dynamic correspondence principle of viscoelasticity in a finite element program to solve boundary value problems simulating uniaxial tension or simple shear and obtains the global complex Young's or shear moduli of the composite.</p>
<p>Each phase of the composite is considered to be thermorheologically simple. The resulting modulus properties of the composite however, are thermorheologically complex and this investigation examines the nature of time-temperature behavior of multi-phase composite materials. The specific composite considered throughout this study contains viscoelastic inclusions embedded in a different viscoelastic matrix material. The deviation of the composite moduli from thermorheologically simple behavior of the matrix material is shown to occur at frequencies and temperatures where the glass-to-rubber transition of the included phases are reached.</p>
<p>Properties of polystyrene and polybutadiene are used to investigate the thermorheological complexity (non-shiftability) of a Styrene-Butadiene-Styrene (SBS) block copolymer. To achieve congruence of the results with experimental data, it is necessary to consider a transition phase of properties "intermediate" to those of styrene and butadiene. Using accurate physical information on the individual phase properties and on the interphase region, it is possible to utilize the numerical model to predict long term properties of multi-phase composites from short term laboratory data. Lacking detailed information on the properties of a particular phase (e.g., the interphase), but knowing the time dependent properties for the composite material at a broad range of temperatures, it is also possible to use the numerical tool to solve an inverse problem and determine the unknown properties of the phase in question.</p>https://resolver.caltech.edu/CaltechETD:etd-10292003-112909General Structural Representations for Multi-Input Multi-Output Discrete-Time FIR and IIR Lossless Systems
https://resolver.caltech.edu/CaltechETD:etd-02222007-083438
Year: 1990
DOI: 10.7907/h011-7b66
<p>Discrete-time lossless systems have been found to be of great importance in many signal processing applications. However, a representation for lossless transfer matrices that spans all such matrices with the smallest possible number of parameters has not been proposed earlier. Existing representations are usually for special cases and therefore not general enough. In this study, two general and minimal representations are presented for multi-input, multi-output FIR and IIR lossless systems. The first representation is in terms of planar rotations and it leads to multi-input, multi-output lattice structures. The second representation is in terms of unit-norm vectors and it enables shorter convergence times in optimization applications. A simple modification of this representation leads to structures that remain lossless under quantization. The structures that follow from these representations share some properties such as the orthogonality of the implementations, and minimality of the number of parameters and scalar delays they are. Since all lossless transfer matrices can be spanned by appropriately adjusting their parameters, these structures can be particularly useful in applications that involve optimization under the constraint of losslessness. Some examples of such applications are included.</p>https://resolver.caltech.edu/CaltechETD:etd-02222007-083438Dynamic Crack Propagation in Elastic-Plastic Solids
https://resolver.caltech.edu/CaltechETD:etd-11062003-112730
Year: 1990
DOI: 10.7907/WHJV-C644
<p>The present finite element study addresses several issues of interest pertaining to the phenomenon of dynamic crack propagation in elastic-plastic solids. Three classes of materials, namely elastic-perfectly plastic materials, linear hardening materials and power-law hardening materials, are considered. The materials are assumed to obey the von Mises yield criterion and the associated flow rule.</p>
<p>Under conditions of Mode I, plane stress, steady state and small scale yielding, we investigated the structures of the near-tip stress and deformation fields. A preliminary asymptotic analysis for crack-tip stress and velocity fields in elastic-perfectly plastic solids was provided to reveal and explain some special features of the crack tip fields observable only in the case of rapid crack propagation. We studied the theoretical basis of a fracture criterion based on the dynamic stress intensity factor for crack growth in materials which fail in a locally ductile manner. We explored the behavior of crack tip fields under non-<i>K</i>-dominance conditions and its effects on the dynamic fracture toughness vs. crack propagation speed relationship.</p>
<p>An Eulerian finite element scheme is employed. Finite element meshes with extremely small elements near the crack tip are carefully designed. The ratio of the crack tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 x 10⁴. In order to overcome numerical difficulties associated with crack-tip strain singularities and the use of small near-tip elements, an efficient stress integration algorithm is devised. The existing stress state determination procedure is modified to prevent the occurrence of negative plastic flow and to avoid mistakenly treating elastic unloading as plastic flow. The above measures are proven to be essential for the convergence of the numerical solution.</p>https://resolver.caltech.edu/CaltechETD:etd-11062003-112730Part I: Forced Generation and Stability of Nonlinear Waves. Part II: Chaotic Advection in a Rayleigh-Bénard Flow
https://resolver.caltech.edu/CaltechETD:etd-02232007-160809
Year: 1990
DOI: 10.7907/2MK9-ZD86
<p>Part I</p>
<p>The forced Korteweg-de Vries model has been found satisfactory in predicting the periodic generation of upstream-advancing solitary waves by a bottom topography moving in a layer of shallow water with a steady transcritical velocity. It is also known that with certain characteristic forcing distributions, there exist waves, according to the fKdV model, which can remain steady in accompanying the characteristic forcing, provided such a wave exists initially, whereas for a different initial condition the phenomenon of periodic generation can still manifest itself. The stability of two such transcritically forced steady solitary waves is investigated, with their bifurcation diagrams determined with respect to the velocity and the amplitude of the forcing as parameters. The linear stability analysis is first carried out; it involves solving a singular, non-self-adjoint eigenvalue problem, which is examined by applying techniques of matched asymptotic expansions with suitable multiscales for singular perturbations, about the isolated bifurcation points of the parameters. The eigenvalues and eigenfunctions for the full range of the parameters are then obtained by numerically summing a power series expansion for the solution. The numerical results, which accurately match with the local analysis, show that the eigenvalues have only four branches σ = ±σ<sub>r</sub> ±iσ<sub>i</sub>. The real part σ<sub>r</sub> is nonvanishing for the velocity less than a certain supercritical value and for the amplitude greater than a certain marginal bound except at a single point in the parametric plane at which the external forcings vanish, reducing the forced waves to the classical free solitary wave. Within this parametric range, the real part of the four eigenvalues is algebraically two to five orders smaller than the imaginary part σ<sub>i</sub>, wherever σ<sub>i</sub> exists; such a small σ<sub>r</sub> indicates physically a weak exponential growth rate of perturbed solutions and mathematically the need of a very accurate numerical method for its determination. Beyond this parametric range, linear stability theory appears to fail because no eigenvalues can there be found to exist. In this latter case a non linear analysis based on the functional Hamiltonian formulation is found to prevail, and our analysis predicts stability. Finally, extensive numerical simulations using various finite difference schemes are pursued, with results providing full confirmation to the predictions made in various regimes by the analysis.</p>
<p>We consider the Korteweg-de Vries equation in the semi-infinite real line with a boundary condition at the origin. The numerical investigations of Chu et al.[2], are revisited and different new forms for the boundary forcing are assumed. In order to provide some qualitative description for the numerical simulations we develop a simple model based on the IST formalism. It is found that the model is also able to provide some quantitative predictions in agreement with the numerical results.</p>
<p>Part II</p>
<p>There has been considerable interest recently on chaotic advection, for the first time explored in the context of Rayleigh-Bénard roll (2D) convection by the experimental work of J. Gollub and collaborators. When the Rayleigh number increases across a (supercritical) value, depending on the wavelength of the rolls, an oscillatory instability sets in. The flow near the onset of the instability can still be modelled by a stream function, which can be split into a time independent part plus a small time dependent perturbation. The motion of fluid particles can therefore be regarded as the flow for a near integrable, "one-and a half" degree of freedom Hamiltonian vector field, with the phase space corresponding to the physical domain. In absence of molecular diffusivity, the evolution of a certain region of phase space can thus be viewed as the motion of a dyed part of fluid, when the tracer is perfectly passive. The most important objects for a theory of transport are the invariant manifolds for the Poincaré map of the flow homoclinic to fixed points, which physically correspond to the stagnation points. As fluid particles cannot cross invariant lines, these curves constitute a sort of "template" for their motion. For the time independent flow, the invariant manifolds connect the stagnation points and define the roll boundaries. Thus, no transport from roll to roll can occur in this case. Switching the perturbation on, these connections are broken and the manifolds are free to wander along the array of rolls. We use segments of stable and unstable manifold to define the time dependent analogue of the roll boundaries. Transport of fluid across a boundary can then be attributed to the way a region bounded by segments of stable and unstable manifold, or "lobe," is evolving under map iterations. This allows us to write explicit formulae for describing the fluid transport in terms of a few of these lobes, for a general cross section defining the Poincaré map. Using the symmetries of special cross sections, we are able to further reduce the number of necessary lobes to just one. Furthermore, these symmetries allow us to derive analytically a lower and upper bound for the first time tracer invades a roll, and a lower bound on the stretching of the interface between dyed and clear fluid. These results are independent of the fact that the perturbation is small. When this is the case however, the analytical tools of the Melnikov and subharmonic Melnikov functions are available, so that an approximation to the lobe areas and location and size of the island bands can be determined analytically. It turns out that in our case these approximations are quite good, even for relatively large perturbations. The results we have produced regarding the strong dependence of transport on the period of the oscillation suggest an effect for which no experimental verification is currently available. The presence of molecular diffusivity introduces a (long) time scale into the problem. We discuss the applicability of the theory in this situation, by introducing a simple rule for determining when the effects of diffusivity are negligible, and perform numerical simulations of the flow in this case to provide an example.</p>https://resolver.caltech.edu/CaltechETD:etd-02232007-160809Aspects of the morphological character and stability of two-phase states in non-elliptic solids
https://resolver.caltech.edu/CaltechETD:etd-01302007-160351
Year: 1991
DOI: 10.7907/WJKM-GB39
Part I. This work focuses on the construction of equilibrated two-phase antiplane shear deformations of a non-elliptic isotropic and incompressible hyperelastic material. It is shown that this material can sustain metastable two-phase equilibria which are neither piecewise homogeneous nor axisymmetric, but, rather, involve non-planar interfaces which completely segregate inhomogeneously deformed material in distinct elliptic phases. These results are obtained by studying a constrained boundary value problem involving an interface across which the deformation gradient jumps. The boundary value problem is recast as an integral equation and conditions on the interface sufficient to guarantee the existence of a solution to this equation are obtained. The contraints, which enforce the segregation of material in the two elliptic phases, are then studied. Sufficient conditions for their satisfaction are also secured. These involve additional restrictions on the interface across which the deformation gradient jumps-which, with all restrictions satisfied, constitutes a phase boundary. An uncountably infinite number of such phase boundaries are shown to exist. It is demonstrated that, for each of these, there exists a solution - unique up to an additive constant - for the constrained boundary value problem. As an illustration, approximate solutions which correspond to a particular class of phase boundaries are then constructed. Finally, the kinetics and stability of an arbitrary element within this class of phase boundaries are analyzed in the context of a quasistatic motion.
Part II. This work investigates the linear stability of an antiplane shear motion which involves a planar phase boundary in an arbitrary element of a wide class of non-elliptic generalized neo-Hookean materials which have two distinct elliptic phases. It is shown, via a normal mode analysis, that, in the absence of inertial effects, such a process is linearly unstable with respect to a large class of disturbances if and only if the kinetic response function - a constitutively supplied entity which gives the normal velocity of a phase boundary in terms of the driving traction which acts on it or vice versa - is locally decreasing as a function of the appropriate argument. An alternate analysis, in which the linear stability problem is recast as a functional equation for the interface position, allows the interface to be tracked subsequent to perturbation. A particular choice of the initial disturbance is used to show that, in the case of an unstable response, the morphological character of the phase boundary evolves to qualitatively resemble the plate-like structures which are found in displacive solid-solid phase transformations. In the presence of inertial effects a combination of normal mode and energy analyses are used to show that the condition which is necessary and sufficient for instability with respect to the relevant class of perturbations in the absence of inertia remains necessary for the entire class of perturbations and sufficient for all but a very special, and physically unrealistic, subclass of these perturbations. The linear stability of the relevant process depends, therefore, entirely upon the transformation kinetics intrinsic to the kinetic response function.
Part III. This investigation is directed toward understanding the role of coupled mechanical and thermal effects in the linear stability of an isothermal antiplane shear motion which involves a single planar phase boundary in a non-elliptic thermoelastic material which has multiple elliptic phases. When the relevant process is static - so that the phase boundary does not move prior to the imposition of the disturbance - it is shown to be linearly stable. However, when the process involves a steadily propagating phase boundary it may be linearly unstable. Various conditions sufficient to guarantee the linear instability of the process are obtained. These conditions depend on the monotonicity of the kinetic response function - a constitutively supplied entity which relates the driving traction acting on a phase boundary to the local absolute temperature and the normal velocity of the phase boundary - and, in certain cases, on the spectrum of wave-numbers associated with the perturbation to which the process is subjected. Inertia is found to play an insignificant role in the qualitative features of the aforementioned sufficient conditions. It is shown, in particular, that instability can arise even when the normal velocity of the phase boundary is an increasing function of the driving traction if the temperature dependence in the kinetic response function is of a suitable nature. Significantly, the instability which is present in this setting occurs only in the long waves of the Fourier decomposition of the moving phase boundary, implying that the interface prefers to be highly wrinkled.https://resolver.caltech.edu/CaltechETD:etd-01302007-160351Active control of the flow past a cylinder executing rotary motions
https://resolver.caltech.edu/CaltechETD:etd-04132004-141454
Year: 1991
DOI: 10.7907/v7p7-d977
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Exploratory experiments have been performed on circular cylinders executing forced rotary motions in a steady uniform flow. These motions include harmonic oscillations, steady rotation, and combinations of the two. Flow visualization and laser-Doppler velocimetry measurements were used to characterize the wake structure, and to estimate the convection speed, spacing, and strength of the vortical structures. Laser-Doppler velocimetry measurements were also made to estimate the cylinder drag coefficient and wake displacement thickness. In addition, the periodic flow close the cylinder and in the near wake region was mapped for a particular forced case. The data show that a considerable amount of control can be exerted over the flow by such means. In particular, a large increase, or decrease, in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation. In order to assess the effects of oscillatory forcing on a cylinder with a net (mean) rotation rate, a novel method for estimating the steady lift forces was employed. Using this method, it was also found that the addition of forced rotary oscillations to the steady rotation of the cylinder helped to increase [...] in the cases where the wake would normally be separated in the steadily rotating case, and decrease it otherwise. Results obtained for a steadily rotating cylinder (no forced oscillations) compare favorably with similar data published in the literature.https://resolver.caltech.edu/CaltechETD:etd-04132004-141454Structural instabilities involving time dependent materials : theory and experiment
https://resolver.caltech.edu/CaltechETD:etd-08082007-100442
Year: 1992
DOI: 10.7907/7h70-2p51
The creep buckling of viscoelastic structures is studied analytically and experimentally to investigate structural stability in the presence of time dependent materials. The theory of linear viscoelasticity is used to model polymeric column specimens subjected to constant compressive end loads. A strength of materials approach (Euler-Bernoulli beam theory) is employed to model the moment-curvature relation for the column. The growth of initial imperfections is calculated using the hereditary integral formulation. Solution techniques are developed for small displacements and then generalized to include the effects of large displacements and rotations. A failure criterion based on maximum deformation allows the column life to be estimated directly from the material relaxation modulus. A discussion generalizing the results to include plates and shells is presented.
Rectangular cross-section polymethylmethacrylate (PMMA) specimens with hinged boundary conditions are used to study viscoelastic buckling experimentally. Constant compressive end loads are applied using a servo-controlled load frame while the specimens are kept in a temperature cabinet at elevated temperatures (accelerating the creep behavior). Specimen shortening and out-of-plane deflections are monitored during the tests. The relaxation modulus of PMMA is approximated by a Prony-Dirichlet series and the model is used to simulate the laboratory experiments. Model and experimental results show good agreement during the "glassy" and slow growth phases of the column response. As the growth rate increases some deviations between theory and experiment are seen. It is shown that the deviations are not a result of geometric nonlinearities, but may, in part, be explained by material nonlinearities not accounted for in the model.
https://resolver.caltech.edu/CaltechETD:etd-08082007-100442On the Existence and Stability of Standing Solitary Waves in Faraday Resonance
https://resolver.caltech.edu/CaltechTHESIS:08182011-080621226
Year: 1992
DOI: 10.7907/fp2g-ds59
A rectangular tank of high-aspect ratio contains a liquid of moderate depth. The tank is subjected to vertical, sinusoidal oscillations. When the frequency of forcing is nearly twice the first natural frequency of the short side of the tank, waves are observed on the free surface of the liquid that slosh across the tank at a frequency equal to one half of the forcing frequency. These sloshing waves are modulated by a slowly varying envelope along the length of the tank. The envelope of the sloshing wave possesses two solitary-wave solutions, the standing soliton corresponding to a hyperbolic-secant solution and the standing kink wave corresponding to a hyperbolic-tangent solution. The depth and width of the tank determine which soliton is present. In the present work, we derive an analytical model for the envelope solitons by direct perturbation of the governing equations. This derivation is an extension of a previous perturbation approach to include forcing and dissipation. The envelope equation is the parametrically forced, damped, nonlinear Schrodinger equation. Solutions of the envelope equations are found that represent the solitary waves, and regions of formal existence are discussed. Next, we investigate the stability of these solitary-wave solutions. A linear-stability analysis is constructed for both the kink soliton and the standing soliton. In both cases, the linear-stability analysis leads to a fourth-order, nonself-adjoint, singular eigenvalue problem. For the hyperbolic-secant envelope, we find eigenvalues that correspond to the continuous and discrete spectrum of the linear operator. The dependence of the continuous-spectrum eigenvalues on the system parameters is found explicitly. By using local perturbations about known solutions and numerically continuing the branches, we find the bound-mode eigenvalues. For the kink soliton, continuous-spectrum branches are also found, and their dependence on the system parameters is determined. Bound-mode branches are found as well. In the case of the kink soliton, we extend the linear analysis by providing a nonlinear proof of stability when dissipation is neglected. We compute numerical solutions of the nonlinear Schrodinger equation directly and compare the results to the previous local analysis to verify the predicted behavior. Lastly, laboratory experiments were performed, examining the stability of the solitary waves, and comparisons are made with the foregoing work. In general, the agreement between the local analysis, the numerical simulations and the experiments is good. However, experiments and direct simulations show the existence of periodic solutions of the envelope equation when bound-mode instabilities are present.https://resolver.caltech.edu/CaltechTHESIS:08182011-080621226Theory and Applications of Hyper-Redundant Robotic Manipulators
https://resolver.caltech.edu/CaltechETD:etd-11082006-132210
Year: 1992
DOI: 10.7907/F12D-0X25
The term "hyper-redundant" refers to robotic manipulators and mobile robots with a very large, possibly infinite, number of actuatable degrees of freedom. These robots are analogous in morphology and operation to snakes, worms, elephant trunks, and tentacles. This thesis presents a novel kinematic framework for hyper-redundant manipulator motion planning and task implementation. The basis of this formulation is the use of a "backbone reference set" which captures the essential macroscopic geometric features of hyper-redundant robots. In the analytical part of this work, the backbone representation is developed and used to solve problems in obstacle avoidance, locomotion, grasping, and "optimal" end effector placement. The latter part of this thesis deals with the design and implementation of a thirty-degree-of-freedom planar hyper-redundant manipulator which is used to demonstrate these novel kinematic and motion planning techniques. Design issues such as robustness with respect to mechanical failure, and design for easy assembly and repair are also addressed. The analytical and design concepts are combined to illustrate tasks for which hyper-redundant robotic mechanisms are well suited.
https://resolver.caltech.edu/CaltechETD:etd-11082006-132210Nonlinear seismic behaviour of steel planar moment-resisting frames
https://resolver.caltech.edu/CaltechTHESIS:10062011-075420910
Year: 1992
DOI: 10.7907/jk1f-2d70
<p>The nonlinear response of steel planar moment-resisting frames during strong earthquakes poses a strong need for accurately modelling inelastic behaviour and large displacements. This thesis attempts to provide realistic and efficient analytical tools to aid this study.</p>
<p>Two large-displacement small-strain beam-column models are employed to include material and geometric nonlinearities. The first model assumes lumped plasticity, and discretises an element into segments. Axial force-Bending Moment strength interaction and flexural bowing are considered. Ten characteristic segment states are identified. An efficient numerical scheme is suggested to solve the nonlinear governing equations. This model only approximately represents the strength and stiffness of beam-columns.</p>
<p>A comprehensive finite element beam-column model is developed to more accurately model the strength and stiffness. A beam-column is discretised into segments, and further, each segment into one-dimensional fibres. A uniaxial cyclic constitutive law valid under arbitrary transient loading is proposed for structural steel. This physically motivated law incorporates the initial yield plateau, and provides explicit expressions for stress in terms of strain throughout the hysteretic path. This law is used to control the hysteretic loading of fibres.</p>
<p>A simple semi-empirical model is employed to analytically describe the highly nonlinear hysteretic behaviour of flexible joint panel zones in steel planar frames. Some modelling assumptions that may be made in frame analyses are evaluated. Numerical study of a building frame with flexible joints indicates that its collapse is sensitive to the joint panel zone design in addition to the ground motion.</p>
https://resolver.caltech.edu/CaltechTHESIS:10062011-075420910An adaptive Lagrangian method for computing 1-D reacting flows, and, The theory of Riemann invariant manifolds for the compressible Euler equations
https://resolver.caltech.edu/CaltechETD:etd-09192007-130342
Year: 1993
DOI: 10.7907/bw0e-2789
In the first part of this thesis, a method for computing one-dimensional, unsteady compressible flows, with and without chemical reactions, is presented. This work has focused on accurate computation of the discontinuous waves that arise in such flows. The main feature of the method is the use of an adaptive Lagrangian grid. This allows the computation of discontinuous waves and their interactions with the accuracy of front-tracking algorithms. This is done without the use of additional grid points representing shocks, in contrast to conventional, front-tracking schemes. The Lagrangian character of the present scheme also allows contact discontinuities to be captured easily. The algorithm avoids interpolation across discontinuities in a natural and efficient way. The method has been used on a variety of reacting and non-reacting flows in order to test its ability to compute complicated wave interactions accurately and in a robust way.
In the second part of this thesis, a new approach is presented for computing multidimensional flows of an inviscid gas. The goal is to use the knowledge of the one-dimensional, characteristic problem for gas dynamics to compute genuinely multidimensional flows in a mathematically consistent way. A family of spacetime manifolds is found on which an equivalent 1-D problem holds. These manifolds are referred to as Riemann Invariant Manifolds. Their geometry depends on the local, spatial gradients of the flow, and they provide locally a convenient system of coordinate surfaces for spacetime. In the case of zero entropy gradients, functions analogous to the Riemann invariants of 1-D gas dynamics can be introduced. These generalized Riemann Invariants are constant on the Riemann Invariant Manifolds. The equations of motion are integrable on these manifolds, and the problem of computing the solution becomes that of determining the geometry of these manifolds locally in spacetime.
The geometry of these manifolds is examined, and in particular, their relation to the characteristic surfaces. It turns out that they can be space-like or time-like, depending on the flow gradients. An important parameter is introduced, which plays the role of a Mach number for the wave fronts that these manifolds represent. Finally, the issue of determining the solution at points in spacetime, using information that propagates along space-like surfaces is discussed. The question of whether it is possible to use information outside the domain of dependence of a point in spacetime to determine the solution is discussed in relation to the existence and uniqueness theorems, which introduce the concept of domain of dependence.
This theory can be viewed as an extension of the method of characteristics to multidimensional, unsteady flows. There are many ways of using the theory to develop practical, numerical schemes. It is shown how it is possible to correct a conventional, second-order Godunov scheme for multidimensional effects, using this theory. A family of second-order, conservative Godunov schemes is derived, using the theory of Riemann Invariant Manifolds, for the case of two-dimensional flow. The extension to three dimensions is straightforward. One of these schemes is used to compute two standard test cases and a two-dimensional, inviscid, shear layer.
https://resolver.caltech.edu/CaltechETD:etd-09192007-130342Experimental and numerical studies on two-dimensional gravity currents in a horizontal channel
https://resolver.caltech.edu/CaltechETD:etd-08232007-094513
Year: 1993
DOI: 10.7907/d44w-pm14
The objective of this investigation is to examine the behavior of two-dimensional gravity currents, especially as applied to the spreading of smoke, generated from a room fire, along a long corridor. Both experimental and numerical techniques were used to provide a model that can adequately explain and predict the behavior of a gravity current under certain boundary conditions.
A series of experiments was carried out to study the effects of Reynolds number on gravity currents in a horizontal water channel. Measurements of the time varying front position, velocity profile of the following current, and the depth of a gravity current were made using either dyed liquids or hydrogen bubble technique. Quantitative results were shown to agree with previously published results. A model was put forth to bridge the gap between the existing models for an inertia-buoyancy dominated gravity current and a viscous-buoyancy dominated one. Comparison between the experimental results and numerical results obtained from the model proved that the model can adequately explain the behavior of the phenomenon.
A second series of experiments was conducted to investigate the behavior of gravity currents in an inclined channel. The quantitative results obtained were less scattered than those obtained in previous research. The gravity current was found to be unsteady in a horizontal channel, while a channel with an angle of inclination of one degree was found to produce a steady flow behind the front of the gravity current. The change of the gravity currents from an unsteady to a steady nature due to the change in the inclination of the channel was found to be gradual and much less abrupt than assumed in previous studies.https://resolver.caltech.edu/CaltechETD:etd-08232007-094513Direct numerical simulations of unsteady separated flows using vortex methods
https://resolver.caltech.edu/CaltechETD:etd-11122003-082957
Year: 1993
DOI: 10.7907/TCQ9-9C86
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Numerical simulations are presented for viscous incompressible flows with and without solid wall boundaries. Our numerical method is based on vortex methods. The classical inviscid scheme is enhanced to account for viscous effects via the method of particle strength exchange. The method is extended to account for the enforcement of the no-slip boundary condition as well by appropriately modifying the strength of the particles. Computations are possible for extended times by periodically remeshing the vorticity field.
The particles are advanced using the Blot-Savart law for the evaluation of the velocity. Computations are made using up to [...](10[superscript 6]) vortex particles by efficiently implementing the method of multipole expansions for vector computer architectures to obtain an [...](N) algorithm.
The method is used to simulate the inviscid evolution of an elliptical vortex in an unbounded fluid as well as unsteady separated flows around circular cylinders for a wide range of Reynolds numbers (40 - 9500). Direct comparisons are made of the results of the present method with those from a variety of theoretical, computational and experimental studies. The results exhibit the robustness and validity of the present method and allow to gain physical insight as to vorticity formation and its relation to the forces experienced by the body.https://resolver.caltech.edu/CaltechETD:etd-11122003-082957Nonlinear effects in interfacial fracture
https://resolver.caltech.edu/CaltechETD:etd-08272007-104817
Year: 1993
DOI: 10.7907/rkt0-7k90
The issue of the non-coplanar quasi-static propagation of a crack in homogeneous and bimaterial sheets is investigated. Through a preliminary linear analysis, it is shown that the interface crack kinking problem is confronted, in most practical cases, with difficulties which do not arise in the homogeneous situation: the crack path as predicted by the maximum energy release rate criterion cannot be determined uniquely and an additional length parameter, absent in the homogeneous case, needs to be specified to assure uniqueness. Following that development, the assumption of small deformations is relinquished and it is shown how the size of the nonlinear zone imparts possibly the physical significance of the additional length parameter. The analysis is performed numerically in the homogeneous and bimaterial cases within the framework of the nonlinearly elastic theory of plane stress and using a "boundary-layer" approach. Material and geometrical nonlinearities are combined through the use of the Generalized Neo-Hookean (GNH) model. As the length of the crack extension becomes comparable to the size of the nonlinear zone, a transition is observed between the value of the energetically most favorable kink angle predicted by the linear theory and a unique "nonlinear" value which is found to be independent of the crack extension length and the far-field loading conditions.
The results of the crack propagation analysis are related to those of a detailed asymptotic analysis of the structure of the near-tip stress and deformation fields for the GNU class of hyperelastic materials. The investigation addresses a) the symmetric (mode I) and non-symmetric (mixed-mode) homogeneous situations, b) the rigid substrate case and c) the general bimaterial problem which allows for an arbitrary choice, on both sides of the interface, of the three material parameters characterizing the GNH model. The asymptotic analysis allows to quantify the effect of the "hardening" characteristics on the blunting of the crack and the associated stress and strain singularities, and shows that the near-tip fields corresponding to a general nonsymmetric loading are, in the homogeneous situation, related to those of the symmetric (mode I) case through a rotation which depends on the material characteristics and the far-field loading conditions. A somewhat similar property is obtained in the bimaterial problem, where the existence of a non-oscillatory and "contact-free" solution is confirmed for all material combinations.https://resolver.caltech.edu/CaltechETD:etd-08272007-104817Dynamic decohesion of bimaterial interfaces
https://resolver.caltech.edu/CaltechETD:etd-12042007-075432
Year: 1994
DOI: 10.7907/36hw-c185
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In the present work, findings of an experimental study of dynamic decohesion of bimaterial systems composed of constituents with a large material property mismatch are presented. PMMA/steel or PMMA/aluminum bimaterial fracture specimens are used. Dynamic one point bend loading is accomplished with a drop weight tower device (for low and intermediate loading rates) or a high speed gas gun (for high loading rates). High speed interferometric measurements are made using the lateral shearing interferometer of Coherent Gradient Sensing in conjunction with high speed photography. Very high crack propagation speeds (terminal crack tip speeds up to [...], where [...] is the shear wave speed of PMMA) and high accelerations ([...], where g is the acceleration of gravity) are observed and reported. Issues regarding data analysis of the high speed interferograms are discussed. The effects of near tip three dimensionality are also analyzed. In crack propagation regions governed by large crack tip accelerations it is found that for accurate analysis of the optical data use of a transient elastodynamic crack tip field is necessary. Otherwise use of a Kd-dominant analysis is sufficient. Using the dynamic complex stress factor histories obtained by fitting the experimental data, a dynamic crack growth criterion is proposed. In the subsonic regime of crack growth it is seen that the opening and shearing displacements behind the propagating crack tip remain constant, i.e., the crack retains a self-similar profile during crack growth at any speed. This forms the basis of the proposed dynamic interfacial fracture criterion. It is also found that the process of dynamic interfacial fracture is highly unstable. This is corroborated by both the very large measured values of crack tip speed and acceleration and by the observation that the energy release rate at the propagating crack tip decreases with increasing crack tip speed. A mechanism of energy transfer from the metal to the PMMA side of the specimen is believed to be responsible for the high transient and transonic effects. An analysis and discussion of this phenomenon is also presented in this work.
https://resolver.caltech.edu/CaltechETD:etd-12042007-075432Continuum dynamics of solid-solid phase transitions
https://resolver.caltech.edu/CaltechETD:etd-10222007-135103
Year: 1995
DOI: 10.7907/PW4M-9B73
<p>This work focuses on the applications in dynamics of recently developed continuum-mechanical models of solid-solid phase transitions. The dynamical problems considered here involve only one space coordinate, and attention is limited to hyperelastic materials that involve two phases. This investigation has two purposes. The first is to determine the predictions of the models in complicated situations. Secondly, the present study attempts to develop analytical and numerical approaches to problems that may be relevant to the interpretation and understanding of experiments involving phase transitions under dynamical conditions.</p>
<p>The first problem studied involves the study of a semi-infinite bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. The end of the bar is suddenly subject to a constant impact velocity that persists for a finite time and is then removed. Interaction between the phase boundary and the elastic waves generated by the impact and subsequent reflections are studied in detail, and the trajectory of the phase boundary is determined exactly. The second task addressed involves the development of a Riemann solver to be applied to the numerical solution of Riemann problems for two-phase elastic materials. Riemann problems for such materials involve complications not present in the corresponding problems that arise, for example, in classical gas dynamics. Finally, a finite-difference method of Godunov type is developed for the numerical treatment of boundary-initial-value problems arising in the model of Abeyaratne and Knowles. The method is applied to specific problems.</p>https://resolver.caltech.edu/CaltechETD:etd-10222007-135103Continuum dynamics of solid-solid phase transitions
https://resolver.caltech.edu/CaltechETD:etd-10222007-135103
Year: 1995
DOI: 10.7907/PW4M-9B73
<p>This work focuses on the applications in dynamics of recently developed continuum-mechanical models of solid-solid phase transitions. The dynamical problems considered here involve only one space coordinate, and attention is limited to hyperelastic materials that involve two phases. This investigation has two purposes. The first is to determine the predictions of the models in complicated situations. Secondly, the present study attempts to develop analytical and numerical approaches to problems that may be relevant to the interpretation and understanding of experiments involving phase transitions under dynamical conditions.</p>
<p>The first problem studied involves the study of a semi-infinite bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. The end of the bar is suddenly subject to a constant impact velocity that persists for a finite time and is then removed. Interaction between the phase boundary and the elastic waves generated by the impact and subsequent reflections are studied in detail, and the trajectory of the phase boundary is determined exactly. The second task addressed involves the development of a Riemann solver to be applied to the numerical solution of Riemann problems for two-phase elastic materials. Riemann problems for such materials involve complications not present in the corresponding problems that arise, for example, in classical gas dynamics. Finally, a finite-difference method of Godunov type is developed for the numerical treatment of boundary-initial-value problems arising in the model of Abeyaratne and Knowles. The method is applied to specific problems.</p>https://resolver.caltech.edu/CaltechETD:etd-10222007-135103Dynamic failure behavior of ceramics under multiaxial compression
https://resolver.caltech.edu/CaltechETD:etd-11032003-101839
Year: 1995
DOI: 10.7907/0NNE-JD20
An experimental technique has been developed that is capable of (1) dynamically loading the specimen in multiaxial compression; (2) controlling the stress state in the specimen in the range from uniaxial stress to uniaxial strain; and (3) allowing the recovery of the sample after loaded by a single, well defined pulse for the characterization of the failure mode. In this technique, cylindrical ceramic specimens were loaded in the axial direction using a split Hopkinson pressure bar modified to apply a single loading pulse, and were confined laterally either by shrink fit sleeves, or by eletro-magnetic force.
Quasi-static and dynamic multiaxial compression experiments have been performed on a machinable glass ceramic, Macor, and a monolithic engineering ceramic, sintered aluminum nitride (A1N). The cylindrical ceramic specimens were confned laterally by shrink fit sleeves: the amount of confining pressure (0-230 MPa) was varied by using different sleeve materials. The quasi-static axial load was applied by a hydraulic driven Material Test System (MTS), whereas the dynamic axial load was provided by a modified split Hopkinson (Kolsky) pressure bar (SHPB). Under both quasi-static and dynamic loading conditions, the experimental results for both materials showed that the failure mode changed from fragmentation by axial splitting under conditions of uniaxial stress (without lateral confinement) to localized deformation on faults under moderate lateral confinement. The fault initiation process was studied experimentally in detail. Based on the experimental results, a compressive brittle failure process was summarized. A transition from brittle to ductile behavior was observed in Macor under high confinement pressure which was achieved using a second sleeve around the inner sleeve. The compressive failure strengths of both materials increased with increasing confinement pressure under both quasi-static and dynamic loading conditions. The highest dynamic compressive strengths of Macor and A1N measured in the experiments were 1.35 GPa and 5.40 GPa, respectively, whereas their quasi-static compressive strength were measured to be 0.43 GPa and 2.5 GPa, respectively.
Based on the experimental results on A1N together with available data in the literature, a failure/flow criterion was developed for ceramic materials under multiaxial loading. A Mohr-Coulomb criterion and an improved Johnson-Holmquist model were found to fit the experimental data for brittle failure, whereas the materials exhibited pressure insensitive plastic flow at high pressures. Observations made in other types of dynamic experiments (e.g., shock wave loading) were rationalized based on the postulated failure mechanisms and the possibility of plastic flow beyond the Hugoniot elastic limit (HEL). The effect of various material properties on the failure behavior was investigated using the proposed failure criterion. The applicability of the present model to a range of ceramics was also explored and the limitations of the model were outlined.
https://resolver.caltech.edu/CaltechETD:etd-11032003-101839Experimental and theoretical aspects of dynamic crack growth along bimaterial interfaces
https://resolver.caltech.edu/CaltechETD:etd-12132007-082556
Year: 1996
DOI: 10.7907/ehea-x787
This work presents findings of an experimental and theoretical study of dynamic bimaterial crack growth. Bimaterial systems composed of constituents with large material mismatch were investigated under dynamic loading conditions. The materials used in this study consisted of Poly-Methylmethacrylate (PMMA) and AISI 4340 Steel, bonded together using a Methylmethacrylate monomer. One point bend loading was achieved using a drop weight tower. Dynamic crack growth, with velocities up to eighty percent of the Rayleigh wave speed of PMMA, was observed using the lateral shearing interferometric technique of Coherent Gradient Sensing (CGS) in conjunction with high speed photography. The results of these experiments are first discussed within the realm of the validity of the linear, elastodynamic asymptotic stress fields. The complex interdependency of stress intensity and mode mixity with crack tip speed is also discussed. The interpretation of |K[superscript d]| and [phi superscript d] in a dynamic bimaterial crack is clarified through the experimental observation of crack growth.
Complications in analysis arising from this interdependency between the dynamic K[superscript d]-field and velocity are examined for experimentally obtained CGS fringe patterns. Improvements of existing analyzing procedures are made, resulting in increased confidence in data obtained utilizing the method of CGS in dynamic bimaterial fracture. Special attention is given to the interaction of loading and velocity in the behavior of these crack tip fields.
Previous methods of investigation have used an elastodynamic, asymptotic K[superscript d]-field to describe the deformations near a bimaterial crack tip. Attempts to develop a fracture criterion based on these results have suffered from the lack of natural length scale as the major criticism. Motivated by experimental observations, a cohesive zone model is presented in this thesis that allows an investigation of dynamic crack growth. The length of the cohesive zone is given by a combination of stress intensity and mixity, bimaterial behavior, and velocity, and emerges as a natural, time evolving length scale with which to examine the bimaterial crack problem. A fracture criterion based on critical cohesive displacements at the trailing edge of the cohesive zone is presented.
This cohesive zone model is subsequently used to examine data obtained from experiment. The model enhances our ability to extrapolate our experimental measurements to the near tip region, and to thus study the neighborhood close to the propagating crack tip. Within experimental error, predictions of the proposed fracture criterion are shown to correspond to the experimentally observed dependence of |K[superscript d]| and [phi superscript d] on the instantaneous crack tip velocity. The fracture criterion based on the cohesive model presented in this paper provides the natural next step in understanding dynamic bimaterial crack growth. It provides a criterion based on physically motivated parameters, introduces a natural length scale into the problem, and increases our understanding of dynamic bimaterial fracture mechanics.
https://resolver.caltech.edu/CaltechETD:etd-12132007-082556The evolution of damage in ceramic matrix composites
https://resolver.caltech.edu/CaltechETD:etd-01072008-112449
Year: 1996
DOI: 10.7907/w4b4-dx66
In an effort to better understand the evolution of damage in brittle matrix composites, the mechanical behavior of a ceramic matrix composite, unidirectional SiC/CAS (SiC fibers reinforcing a calcium aluminosilicate matrix), was studied. The presented results are based on uniaxial tension experiments for specimens with the fibers aligned in the loading direction. Post-test optical and scanning electron microscopy was also used to identify the various micromechanisms of damage; axial and transverse strain gauges on all four gage section surfaces and in situ acoustic emission and ultrasonic wave speed measurements were used to monitor the evolution of damage. The experimental results demonstrate the existence of "zones of deformation" which are associated with the onset of different damage mechanisms. The energy dissipated in each of these zones was calculated. It is shown that the observed stress-strain behavior can be qualitatively explained in terms of the material properties of the matrix and the fiber, the material processing, and the postulated zones of deformation.
The experimental results for SiC/CAS were compared with an existing shear-lag model, and the shortcomings of the model are discussed. By approximating matrix cracks as penny shaped cracks, a micromechanical model was used to estimate the change in the axial modulus of the composite. These results also present another way to interpret the acoustic emission data.
The evolution of damage in the SiC/CAS experiments was found to be strain rate dependent even within the quasi-static strain rate regime. For higher rate experiments, the transition from elastic to matrix cracked occurred at a stress level that was nearly twice that of the same transition in the lower rate experiments. This phenomenon and the mechanisms which cause it was further investigated with a model material system (a brittle epoxy resin sandwiched between aluminum strips). In situ quantification of the stress during damage initiation and propagation was realized by the optical method of Coherent Gradient Sensing. Based on these results, the reasons for strain rate dependence of the composite are postulated.
Detailed understanding of aspects of the evolution of in brittle matrix composites was achieved with finite element simulations. This modeling was based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). After failing, the cohesive elements could slide with Coulomb friction. The tension and shear aspects of failure were uncoupled. The cohesive elements were used to simulate a Dugdale penny shaped crack in a homogeneous cylinder; results compared well to the analytical solution. In order to solve the composite axisymmetric unit cell problem, inertia and viscous damping were added to the formulation. The resulting dynamic problem was solved implicitly using the Newmark Method. Results were compared to the experiment by assuming that only a given number of unit cells were active at any point during the simulation. The effects of changing material properties (e.g., interface strength and toughness and matrix toughness) and loading rate are discussed. Several aspects of the experimentally observed material response of SiC/CAS composite were reproduced by the numerical simulations.
https://resolver.caltech.edu/CaltechETD:etd-01072008-112449Dynamics of phase transformations in thermoelastic solids
https://resolver.caltech.edu/CaltechETD:etd-02042008-151022
Year: 1997
DOI: 10.7907/gk0c-8r75
The dynamical aspects of solid-solid phase transformations are studied within the framework of the theory of thermoelasticity. The main purpose is to analyze the role of temperature in the theory of phase transitions. This investigation consists of two parts: first, it is shown that by imposing a kinetic relation and a nucleation criterion it is possible to single out a unique solution to the Riemann problem for an adiabatic process. This extends to the thermomechanical case results previously found in a purely mechanical context. Secondly, based on an admissibility criterion for traveling wave solutions within the context of an augmented theory that includes viscosity, strain gradient and heat conduction effects, a special kinetic relation is derived using singular perturbation techniques.
https://resolver.caltech.edu/CaltechETD:etd-02042008-151022Measurement of the dynamic bulk compliance of polymers
https://resolver.caltech.edu/CaltechETD:etd-01082008-112920
Year: 1997
DOI: 10.7907/vxb1-4950
Measurements are described and analyzed for the determination of the dynamic bulk compliance for polyvinyl acetate) [PVAc] as a function of frequency and temperature. The real and imaginary parts of the dynamic bulk compliance over the frequency range from 10 Hz to 1,000 Hz have been measured at different temperatures by determining the compressibility of a specimen confined to an oil-filled cavity via pressurization by a piezoelectric driver and response of a piezoelectric sensor. The wavelength of the compressional wave generated by the piezoelectric transducer over the frequency range used is much larger than the size of the cavity so that the pressure can be considered uniform inside the cavity. The complex compliances of the specimen, confining liquid, and the cavity, are additive upon the pressure variations due to the piezoelectric transducer expansion and contraction. All deformations are considered to be purely dilitational.
A master compliance curve over a total frequency range of about 12 decades is generated by the method of time-temperature superposition. Experimental problems addressing limitations in resolution capability are discussed. The results are compared with the classical measurements obtained by McKinney and Belcher over thirty years ago. Further comparison of the bulk with shear compliance data shows that the extent of the transition ranges for the shear and for the bulk functions are comparable, but the two transitions belong to different time scales: That of the bulk response falls mostly into the glassy domain of the shear behavior. One concludes thus that for linearly viscoelastic response the molecular mechanisms contributing to shear and bulk deformations have different conformational sources.
https://resolver.caltech.edu/CaltechETD:etd-01082008-112920Shock Wave Processing of Transitional Metal Silicides
https://resolver.caltech.edu/CaltechETD:etd-09202002-154801
Year: 1998
DOI: 10.7907/9g63-5c59
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Shock wave consolidation is an innovative processing technique for the densification of initially porous media. A compressive shock wave is introduced in the material by the impact of a high velocity flyer plate. Densification is achieved via intense inhomogeneous plastic deformation, pore collapse, and localized melting around particle surface. The passage of the shock wave may also induce chemical reactions within the material. The chemical reactivity of the powders are enhanced through dislocation nucleation, plastic flow, grain fracture and mass mixing as a result of the shock wave.
A systematic investigation is performed to examine the effects of particle size and porosity on the initiation of the Ti[subscript 5]Si[subscript 3] reaction from the elemental powder mixture (i.e., 5 Ti + 3 Si). The initial powder porosity is varied from 40% to 49% of the theoretical density for two different size powders. The threshold shock energy necessary for complete silicide reaction is established. The powders are consolidated with shock energies up to 671 J/g and shock pressures up to 7.3 GPa. The threshold shock energy for the large powder mixture is found to be approximately 80% higher than that for the smaller powder mixture. For both sized powders, an increase in the threshold shock energy of 75% is observed in decreasing the initial porosity of the powders from 49% to 40%. Evidence for the reaction of solid Ti and liquid Si is observed in isolated regions at shock energies slightly below the threshold energy.
Mechanical alloying and shock wave consolidation are examined as viable alternatives for the synthesis and consolidation of MoSi [subscript 2]. Mechanic alalloying of Mo + 2Si is monitored with X-ray diffraction and differential scanning calorimetry (DSC). The milling time is varied from two hours to one hundred forty-four hours. Nanocrystalline MoSi [subscript 2] is observed after sixteen hours of ball milling. X-ray diffraction is used to follow the extent of alloying and average grain size as a function of ball milling time. DSC is utilized to determine the onset endothermic and exothermic reactions in the ball milled powder. MoSi [subscript 2] is produced from the elemental powder mixture by shock wave consolidation.https://resolver.caltech.edu/CaltechETD:etd-09202002-154801I. High pressure melting of [gamma]-iron and the thermal profile in the Earth's core. II. High pressure, high temperature equation of state of fayalite (Fe2SiO4)
https://resolver.caltech.edu/CaltechETD:etd-02262007-141751
Year: 1998
DOI: 10.7907/z7r2-xf47
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The melting curve of [...]-iron in the pressure range of 100 to 300 GPa has been derived by computing Gibbs free energies at high pressures and high temperatures from thermodynamic and equations of state (EOS) data for the [...], [...] and liquid-phases. Our calculations indicate the melting curve of iron is very sensitive to the EOS of both the solid [...] and melt phase. Our best estimate of the EOS parameters for [...]-iron are: p0 = 8.775 ± 0.012 Mg/m3, [...] = 205 ± 4 GPa, [...] = 4.80 ± 0.01 (referenced to 12 GPa and 300 K). The calculation favors the melting curve of Boehler [1993] or Saxena et al. [1993]. Shock-wave experiments on pure iron preheated to 1573 K were conducted in 17-73 GPa range. The shock-wave equation of state of [gamma]-iron at 1573 K initial temperature can be fit with [...] = 4.102(0.015) km/s + 1.610(0.014)[...] with [...] = 7.413 ± 0.012 Mg/m3. [Gamma]-iron's bulk modulus and its pressure derivative are 124.7±1.1 GPa and 5.44±0.06 respectively.
We present new data for sound velocities in the [gamma]- and liquid-phases. In the [gamma]-phase, to a first approximation, the longitudinal sound velocity is linear with respect to density: Vp = -3.13(0.72) + 1.119(0.084) [...] (units for Vp and [...] are km/s and Mg/m3 respectively). Melting was observed in the highest pressure (about 70-73 GPa) experiments at a calculated shock temperature of about 2775 ± 160 K. This result is consistent with our calculated [...]-iron melting curve which is close to those measured by Boehler [1993] and Saxena et al. [1993]. The liquid iron sound velocity data yield a Gruneisen parameter value for liquid iron of 1.63±0.28 at 9.37±0.02 Mg/m3 at 71.6 GPa. The quantity [...] from our data is 15.2±2.6 Mg/m3, which is within the bounds of Brown and McQueen [1986] (13.3-19.6 Mg/m3). Based on upward pressure and temperature extrapolation of our melting curve of [gamma]-iron, the estimated inner core-outer core boundary temperature is 5500±400 K, the temperature at the core-mantle boundary on the outer core side is about 3930±630 K, and the thermal boundary layer at the core-mantle boundary has a temperature difference between 400 and 1400 K.
The shock-wave equation of state of initially solid (300 K) and molten (1573 K) fayalite (Fe2SiO4, Fa) are reported in the ranges 23 to 212 GPa and 5 to 47 GPa, respectively. The 300 K data appear to undergo a phase change in the 35-55 GPa range. The density of the high pressure phase (HPP) is consistent with a dense oxide mixture. Although the initially 300 K fayalite may melt along its Hugoniot, this is not explicitly detected. Fitting the HPP Hugoniot data in the shock velocity ([...])-particle velocity ([...]) plane yields:
[...] = 4.375(0.027) Mg/m3, (1)
[...] = 4.07(0.22) km/s + 1.43(0.06) [...], (2)
where [...] is the initial density. The isentropic bulk modulus [...] = 72.4 ± 8.0 GPa, and its pressure derivative [...] = 4.72±0.24.
The 1573 K data set yields:
[...] = 3.750(0.018) Mg/m3, (3)
[...] = 2.63(0.02) km/s + 1.59(0.01) [...], (4)
and [...] = 25.9 ± 0.4 GPa, [...] = 5.36 ± 0.04. The bulk modulus compares favorably with Agee [1992a]'s result (24.4 GPa), but the pressure derivative is quite different (10.1 from Agee [1992a]).
Above 50 GPa, the high pressure regime of the Hugoniot of the solid fayalite can be fit with oxide mixture models using stishovite and FeO (either LPP or HPP). The fayalitic liquid compression data above 40 GPa are well fit with ideal mixing of partial molar volumes of stishovite and FeO (LPP or HPP), in support of the hypothesis of Rigden et al. [1989].
A model basalt incorporating the liquid fayalite data shows the neutral buoyancy zone of basic silicate melts of plausible terrestrial compositions is at about 250-400 km depth based on the PREM Earth model.
https://resolver.caltech.edu/CaltechETD:etd-02262007-141751Modeling and Experiments for a Class of Robotic Endoscopes
https://resolver.caltech.edu/CaltechETD:etd-10112006-154843
Year: 1999
DOI: 10.7907/NG6V-TD44
<p>Current developments in minimally invasive medical practice motivated this study of self-propelled, robotic endoscopes for deep penetration into curved physiological lumens. The conceptual design of such devices is applicable to endoscopy within a variety of lumens in the human body, e.g., blood vessels, but the initial objective of this technology is to provide access to the interior of the entire small intestine without surgical incisions. The small intestine presents several challenges to endoscopic penetration: it is extremely compliant to applied loading, internally lubricated, easily injured, and contains many tight curves along its length of approximately eighteen feet.</p>
<p>This thesis reports the basic design and locomotion concepts for one class of endoscopic robots that are intended to provide safe and reliable traversal of the small intestine via worm-like actuation. Five generations of proof-of-concept prototype robots have been built to validate the fundamental concepts. Furthermore, these miniaturized robots have incorporated the following features: redundant actuation with computer control, tool-free modular assembly, and on-board videoimaging capability. The prototypes have been tested in rubber tubing, the small intestines of deceased pigs, and in the small intestines of live, anaesthetized pigs.</p>
<p>At the onset of this research, little regarding the elastic properties of small intestine existed in the biomechanics literature that would be applicable to the design of these mechanisms. However, accurate prediction of the small intestine's response to robotic loadings would dramatically improve the research and development process of these machines. Thus, an investigation of the elastic behavior of the small intestine commenced. Finite deformation, nonlinear, anisotropic, incompressible, viscoelastic behavior of the small intestine was studied. This soft tissue biomechanical analysis and experimentation (on living and dissected intestinal specimens) culminated with a numerical model that simulates intestinal response to the actions of a prototypical robotic component. Experiments on living specimens were performed to determine the levels of applied loadings and internal stresses that are likely to injure these fragile tissues, and the biomechanics computer modeling incorporates three distinct measures for injury potential.</p>https://resolver.caltech.edu/CaltechETD:etd-10112006-154843Impact-Induced Phase Transformations in Elastic Solids: A Continuum Study Including Numerical Simulations for GeO₂
https://resolver.caltech.edu/CaltechETD:etd-02262008-153435
Year: 1999
DOI: 10.7907/4dhf-fj83
<p>This thesis applies recently developed continuum theories of diffusionless phase transformations in solids to the study of impact problems involving materials which can experience such phase changes. Our objective is to compare the theoretical predictions against certain experimental results.</p>
<p>In the experiments of interest, a face-to-face impact occurs between a disk of amorphous germanium dioxide and another material, either tungsten or an aluminum alloy. The GeO₂ is believed to transform to another phase if sufficient compressive stress is achieved.</p>
<p>We model these experiments using one-dimensional finite elasticity. Phase-changing materials are represented by non-convex potential energy functions. This can produce phase boundaries that propagate <i>subsonically</i> or <i>supersonically</i> with respect to the slower longitudinal wave speed of the two phases. When a subsonic phase boundary is possible, it is not uniquely determined by the fundamental field equations and jump conditions. Uniqueness is obtained by invoking a <i>nucleation criterion</i> to control the initiation of the new phase, and a <i>kinetic relation</i> to govern its evolution.</p>
<p>The experiments considered here are sufficiently long in duration (≈ 3 µs) that several reflections and wave interactions occur, and the analysis becomes analytically intractable. Accordingly, a finite-difference method of Godunov type is employed to analyze these experiments numerically. Methods of Godunov type treat adjoining discretized spatial elements as the two sides of a Riemann problem, which is typically solved <i>approximately</i> by linearizing around the initial conditions on each side. Fortuitously, all constitutive models employed in this thesis are such that the required Riemann problems can be solved <i>exactly</i> without too much effort.</p>
<p>Simulations utilizing the numerical method demonstrate that the impact response of a material is sensitive to the kinetic relation that enters the model. It appears the theory may offer a plausible description of the experiments, though the restrictions placed on the constitutive models herein seem too severe to provide a good quantitative match to the experimental results.</p>https://resolver.caltech.edu/CaltechETD:etd-02262008-153435Shape-memory effect in bulk and thin-film polycrystals
https://resolver.caltech.edu/CaltechETD:etd-02212008-114547
Year: 1999
DOI: 10.7907/4NW5-3Q89
Shape-memory effect (SME) is a phenomenon where deformation suffered below a critical temperature can be recovered on heating. About 20-30 alloys are known to exhibit SME in single crystals. However, the degree to which they retain their shape-memory behavior in polycrystals is widely varied. In particular, Ti-Ni and Cu-Zn-Al undergo cubic to monoclinic transformation and recover similar strains as single crystals; yet, the observed shape-memory behavior in the former is much better than that in the latter. We develop a model based on energy minimization to understand this difference. Using this model, we establish that texture is the very important reason why the strains recoverable in Ti-Ni are so much larger than those in Cu-based shape-memory alloys in rolled, extruded and drawn specimens. We find that even the qualitative behavior of combined tension-torsion can critically depend on the texture. The results are in good agreement with experimental observations.
We extend our analysis to the behavior of very thin films with three competing length scales: the film thickness, the length scales of heterogeneity and material microstructure. We start with three-dimensional nonhomogeneous nonlinear elasticity enhanced with an interfacial energy of the van der Waals type, and derive the effective energy density as all length scales tend to zero with given limiting ratios. We do not require any priori selection of asymptotic expansion or ansatz in deriving our results. Depending on the dominating length scale, the effective energy density can be identified by three procedures: averaging, homogenization and thin-film limit. We apply our theory to martensitic thin films and use a model example to show that the shape-memory behavior can crucially depend on the relative magnitudes of these length scales. Using this theory, we show that sputtering textures in both Ti-Ni and Cu-based shape-memory thin films are not favorable for large recoverable strain. We comment on multilayers made of shape-memory and elastic materials.
Finally, we suggest textures for improved SME in bulk and thin-film polycrystals.https://resolver.caltech.edu/CaltechETD:etd-02212008-114547The Influence of Oxygen Vacancies on Domain Patterns in Ferroelectric Perovskites
https://resolver.caltech.edu/CaltechETD:etd-01032005-140446
Year: 2005
DOI: 10.7907/5QSX-9Y68
<p>This thesis investigates the role of oxygen vacancies in determining ferroelectric properties and domain patterns of ferroelectric perovskites. Being non-polar (paraelectric) above their Curie temperature but spontaneously polarized (ferroelectric) below it, ferroelectric perovskites offer a tantalizing potential for applications: large actuation through domain switching and memory storage via switchable electric polarization. Oxygen vacancies, commonly present and mobile at high temperature, are the primary defects and thus play a central role in these applications.</p>
<p>We develop a model that combines the ferroelectric and semiconducting nature of ferroelectric perovskites. Oxygen vacancies act as n-type dopants and thus affect the semiconducting properties. We show that the ferroelectric and semiconducting features interact and lead to the formation of depletion layers near the electrodes and double layers at the 90° domain walls. We find a potential drop across 90° domain walls even in a perfect crystal. This potential drop marks the essential difference between a 90° and an 180° domain wall, drives the formation of a space charge double layer in a doped crystal, promotes electronic charge injection and trapping, and leads to the redistribution of oxygen vacancies at 90° domain walls. The rearrangement of oxygen vacancies near 90° domain walls may form a basis for domain memory and provides a potentially new mechanism for large electrostriction.</p>
<p>We also rigorously justify the continuum theory by calculating the Coulomb energy of a spontaneously polarized solid starting from a periodic distribution of charges based on the classical interpretation of ferroelectrics and with a definite choice of polarization per unit cell. We prove that in the limit where the size of the body is large compared to the unit cell, the energy of Coulombic interactions may be approximated by a sum of a local part and a nonlocal part. The local part depends on the lattice structure, but is different from the Lorentz formula for a lattice of dipoles. The nonlocal part is identical to the Lorentz formula.</p>https://resolver.caltech.edu/CaltechETD:etd-01032005-140446Atomic Structure of Ferroelectric Domain Walls, Free Surfaces and Steps
https://resolver.caltech.edu/CaltechETD:etd-12142004-121255
Year: 2005
DOI: 10.7907/jdy3-1m77
The goal of this thesis is to develop a general framework for lattice statics analysis of defects in ferroelectric Perovskites. The techniques presented here are general and can be easily applied to other systems as well. We present all the calculations and numerical examples for two technologically important ferroelectric materials, namely, PbTiO3 and BaTiO3. We use shell potentials, that are derived using quantum mechanics calculations, and analyze three types of defects: (i) 180° and 90° domain walls, (ii) free surfaces and (iii) steps in 180° domain walls. Our formulation assumes that an interatomic potential is given. In other words, there is no need to have the force constants or restrict the number of nearest neighbor interactions a priori. Depending on the defect and symmetry, the discrete governing equations are reduced to those for representatives of some equivalence classes. The idea of symmetry reduction in lattice statics calculations is one of the contributions of this thesis. We call our formulation of lattice statics 'inhomogeneous lattice statics' as we consider the fact that close to defects force constants (stiffness matrices) change. For defects with one-dimensional symmetry reduction we solve the discrete governing equations directly using a novel method in the setting of the theory of difference equations. This will be compared with the solutions obtained using discrete Fourier transform. For defects with two-dimensional symmetry reduction we solve the discrete governing equations using discrete Fourier transform. We calculate the fully nonlinear solutions using modified Newton-Raphson iterations and call the method 'inhomogeneous anharmonic lattice statics'. This work is aimed to fill the gap between quantum mechanics ab initio calculations and continuum models (based on Landau-Ginzberg-Devonshire theory) of ferroelectric domain walls.https://resolver.caltech.edu/CaltechETD:etd-12142004-121255Experimental Study of Dynamic Frictional Sliding Modes along Incoherent Interfaces
https://resolver.caltech.edu/CaltechETD:etd-01162006-005552
Year: 2006
DOI: 10.7907/0CCJ-5S66
<p>Dynamic sliding along incoherent (frictional) interfaces is investigated experimentally in a microsecond time scale. A bimaterial system comprised of Homalite and steel plates and a homogeneous system consisting of two Homalite plates are considered. The plates are held together by a uniform compressive stress while dynamic sliding is initiated by an impact-induced shear loading. The evolution of maximum shear stress contours is recorded by high-speed photography in conjunction with dynamic photoelasticity. Simultaneously with photoelasticity, a newly-developed technique based on laser interferometry is employed to locally measure the sliding speed at the interface.</p>
<p>The response of the Homalite-steel bimaterial system differs according to whether the impact loading is applied to the Homalite plate or to the steel plate. In the first case, a disturbance traveling along the interface at a constant speed close to the Rayleigh wave speed of steel generates a shear Mach line crossing the P-wave front. Sliding initiates behind the P-wave front in the Homalite plate and it propagates at a supershear speed with respect to the shear wave speed of Homalite. A disturbance, traveling at constant speeds between the shear wave speed and the longitudinal wave speed of Homalite, appears behind the sliding tip. Wrinkle-like opening pulses, propagating along the bimaterial interface at a constant speed between the Rayleigh wave and the shear wave speed of Homalite, are also observed. When the impact loading is applied to the steel plate, sliding at a given point initiates with the arrival of the P-wave front there, so that the rupture is sonic with respect to steel and supersonic with respect to Homalite.</p>
<p>In all the experiments performed on the bimaterial structure (Homalite-steel), sliding always occurred in a crack-like mode. In the case of a homogeneous system of Homalite plates however, direct physical evidence of different modes of sliding is recorded. Crack-like sliding, pulse-like sliding and mixed mode sliding in the form of pulses followed by a crack are discovered. Supersonic trailing pulses are also recorded. Behind the sliding tip, wrinkle-like opening pulses are developed for a wide range of impact speeds and confining stresses.</p>
https://resolver.caltech.edu/CaltechETD:etd-01162006-005552A Micromechanics-Inspired Three-Dimensional Constitutive Model for the Thermomechanical Response of Shape-Memory Alloys
https://resolver.caltech.edu/CaltechETD:etd-05112006-162948
Year: 2006
DOI: 10.7907/MB1W-1V17
<p>The goal of this thesis is to develop a full dimensional micromechanics-inspired constitutive model for polycrystalline shape-memory alloys. The model is presented in two forms: (1) The one-dimensional framework where we picture the ability of the model in capturing main properties of shape memory alloys such as superelasticity and shape-memory effect; (2) The full dimensional model where micromechanics origins of the model, the concepts emerged from those analysis and their relation to macroscopic properties in both single and polycrystals are presented.</p>
<p>We use this framework to study the effects of the texture and anisotropy in the material behavior. Since phase transformation often competes with plasticity in shape-memory alloys, we incorporate that phenomenon into our model. We also demonstrate the ability of the model to predict the response of the material and track the phase transformation process for multi-axial, proportional and non-proportional loading and unloading experiments. We consider both stress-controlled and strain-controlled experiments and develop the model for isothermal, adiabatic and non-adiabatic thermal conditions. Adiabatic heating and loading rate both lead to the apparent hardening at high rates. We also visit this problem and examine the relative role of these two factors.</p>
<p>Finally we extend our model to study the reversible "bcc" to "hcp" martensitic phase transformation in pure iron. We consider a wide range of loading rates ranging from quasistatic to high rate dynamic loading and use our model to describe the evolution of the microstructure along with the effects of the rate hardening and thermal softening.</p>https://resolver.caltech.edu/CaltechETD:etd-05112006-162948Nonlocal Microstructural Mechanics of Active Materials
https://resolver.caltech.edu/CaltechETD:etd-06122006-161234
Year: 2007
DOI: 10.7907/YGR6-H428
<p>This thesis deals with two aspects of the mechanics of symmetry-breaking defects such as phase boundaries, inclusions and free surfaces, and their role in the macroscopic response of active materials. We first examine the problem of kinetics using a nonlocal theory, and then study the role of geometry in active materials with fields that are not confined to the material.</p>
<p>Classical PDE continuum models of active materials are not closed, and require nucleation and kinetic information or regularization as additional constitutive input. We examine this problem in the peridynamic formulation, a nonlocal continuum model that uses integral equations to account for long-range forces that are important at small scales, and allows resolution of the structure of interfaces. Our analysis shows that kinetics is inherent to the theory. Viewing nucleation as a dynamic instability at small times, we obtain interesting scaling results and insight into nucleation in regularized theories. We also exploit the computational ease of this theory to study an unusual mechanism that allows a phase boundary to bypass an inclusion.</p>
<p>Shifting focus to problems of an applied nature, we consider issues in the design of ferroelectric optical/electronic circuit elements. Free surfaces and electrodes on these devices generate electrical fields that must be resolved over all space, and not just within the body. These fields greatly enhance the importance of geometry in understanding the electromechanical response of these materials, and give rise to strong size and shape dependence. We describe a computational method that transforms this problem into a local setting in an accurate and efficient manner. We apply it to three examples: closure domains, a ferroelectric slab with segmented electrodes and a notch subjected to electro-mechanical loading.</p>https://resolver.caltech.edu/CaltechETD:etd-06122006-161234Combined Experimental and Numerical Study of Spontaneous Dynamic Rupture on Frictional Interfaces
https://resolver.caltech.edu/CaltechETD:etd-10242008-070701
Year: 2009
DOI: 10.7907/BGGT-MC04
<p>The process of spontaneous dynamic frictional sliding along the interface of two elastic solids is of great interest to a number of disciplines in engineering and sciences. Applications include frictional rupture processes in earthquakes, delamination of layered composite materials, and sliding between soft membranes in biological systems. The transient nature of rupture dynamics presents an array of fascinating yet challenging questions, including the nucleation process, the mechanism of interface failure, and the speed and mode of rupture propagation.</p>
<p>This thesis presents such a combined experimental and theoretical study aimed at understanding the conditions for selecting pulse-like vs. crack-like rupture modes and subshear vs. supershear rupture speeds. There are two major contributions in this work. The first one is high-resolution experimental study of the rupture modes on a frictional interface. The study presents first experimental observations of spontaneous pulse-like ruptures in a homogeneous linear-elastic setting that mimics crustal earthquakes, reveals how different rupture modes are selected based on the level of fault prestress, demonstrates that both rupture modes can transition to supershear speeds, and advocates, based on comparison with theoretical studies, importance of velocity-weakening friction for earthquake dynamics. The second major contribution is the numerical modeling of the rupture experiments that reveal the importance of the rupture nucleation mechanism and friction formulations. The modeling of sub-Rayleigh to supershear transition has demonstrated the influence of rupture nucleation mechanism on supershear transition distance, as well as on the mechanism of supershear transition. The modeling of pulse-like to crack-like rupture mode transition has confirmed the necessity of velocity weakening friction for producing pulse-like rupture to match the experimental observations.</p>
https://resolver.caltech.edu/CaltechETD:etd-10242008-070701